WASHINGTON—President Trump and his company’s chief financial officer coordinated with Michael Cohen to pay for the silence of a porn star and conceal Mr. Trump’s role in the deal, using sham invoices to cover it up, Mr. Cohen alleged in testimony to the House Oversight Committee.

As part of his testimony on Wednesday, Mr. Cohen showed lawmakers an Aug. 1, 2017, check to him signed by President Trump, and another signed by his son Donald Jr. and Allen Weisselberg, the Trump Organization’s CFO. He said they were related to the $130,000 payment he made to conceal an alleged sexual encounter between Mr. Trump and Stephanie Clifford, the porn star known as Stormy Daniels.

The checks, Mr. Cohen said, were part of monthly installments to reimburse him for paying Ms. Clifford just before the 2016 presidential election and were falsely identified as “legal expenses” to conceal the president’s involvement after The Wall Street Journal first reported the payment in January 2018.

Mr. Cohen, Mr. Trump’s former lawyer, also testified in detail about his discussions with Messrs. Trump and Weisselberg as they considered making the Clifford payment in October 2016.

Mr. Trump, who is in Vietnam for a summit with North Korean leader Kim Jong Un, lashed out at Mr. Cohen on Twitter Wednesday morning. “Michael Cohen…was just disbarred by the State Supreme Court for lying & fraud. He did bad things unrelated to Trump. He is lying in order to reduce his prison time,” Mr. Trump wrote. Republicans on the committee made similar charges against Mr. Cohen, who has pleaded guilty to lying to Congress.

A lawyer for Mr. Weisselberg declined to comment. The Trump Organization didn’t respond to a request for comment.

In a remarkable 5½-hour spectacle, Mr. Cohen offered fresh allegations under oath on issues that have dominated the political, legal and media worlds. He said Mr. Trump knew ahead of time that WikiLeaks was going to dump Democratic National Committee emails damaging to his rival for the presidency, Hillary Clinton, and that Mr. Trump continued to discuss a project to build a Trump Tower in Moscow well into 2016, contradicting Mr. Cohen’s own testimony before Congress in 2017.

He also alleged that Mr. Trump frequently misrepresented his wealth to banks, insurance companies and tax authorities to his own advantage.

The hearing, peppered throughout with partisan bickering, presented the 52-year-old Mr. Cohen—who had long worked behind the scenes as Mr. Trump’s “fixer”—to much of the public for the first time. Mr. Cohen, his hands often clasped and brows furrowed, spoke slowly and steadily in a thick New York accent. As he read 20 pages of his prepared testimony, he paused for effect as he described Mr. Trump as a “racist...a con man…a cheat.” As the hearing concluded, he wiped away a tear at the mention of his daughter.

Republicans sought to portray the former Trump lawyer as a man scorned and a liar, noting that he pleaded guilty to crimes beyond the hush-money payments, including multiple-year tax fraud.

Republican lawmakers from the House Oversight Committee repeatedly questioned Michael Cohen on his motives and credibility as a witness. Photo: AP

Rep. Jim Jordan (R., Ohio) suggested Mr. Cohen’s testimony was fueled by his bitterness about not getting a White House job, an assertion Mr. Cohen denied. Rep. Paul Gosar (R., Ariz.) told him: “You’re a pathological liar. You don’t know truth from falsehood.”

The Democratic chairman of the committee, Rep. Elijah Cummings of Maryland, while warning Mr. Cohen about his previous lies to Congress, accused Republicans of trying to silence Mr. Cohen. “The days of this committee protecting the president at all costs are over. They’re over,” Mr. Cummings said.

Mr. Cohen testified that he had about 100 tapes of clients other than Mr. Trump, and that Mr. Trump asked him to threaten individuals or entities “probably” 500 times over the past decade.

Mr. Cohen’s testimony offered little new specifics on allegations that Mr. Trump and his associates colluded with Russia during the presidential election. It did provide some clues into the continuing probe by the Manhattan U.S. attorney’s office into the financial dealings of the Trump Organization.

Asked whether he was aware of any additional illegal acts or wrongdoing by Mr. Trump that he hadn’t previously discussed, Mr. Cohen said he was—but that those matters were under investigation by federal prosecutors in Manhattan. He also said prosecutors had asked him not to discuss his most recent conversation with Mr. Trump and his associates, which he said was under investigation.

A check signed in August 2017 by President Trump to Michael Cohen, who said it was part of the reimbursement for his October 2016 $130,000 hush-money payment to Stephanie Clifford.

The day marked the most extensive account to date of Mr. Trump’s alleged involvement in a hush-money pact with a porn star, and for the first time publicly implicated one of Mr. Trump’s longest-serving aides, Mr. Weisselberg.

Mr. Cohen first publicly implicated the president in the hush-money scheme in August, when he alleged that Mr. Trump had directed him to arrange the payment. On Wednesday, he said he conferred with Mr. Trump about the payment multiple times before the then-candidate ultimately decided to pay off Ms. Clifford. Mr. Cohen said Mr. Trump told him: “It’s $130,000. It’s not a lot of money. And we should just do it. So go ahead and do it.”

Mr. Trump then directed Mr. Cohen and Mr. Weisselberg to “figure out how” to arrange the payment, Mr. Cohen said. He said Mr. Trump directed him to use his personal funds “to avoid any money being traced back to him that could negatively impact his campaign.”

Mr. Trump has denied directing his lawyer to break the law.

Mr. Cohen said he asked Mr. Weisselberg to pay Ms. Clifford, and that Mr. Weisselberg responded that he couldn’t. The two then discussed whether it would be possible to route the payment through one of Mr. Trump’s properties, Mr. Cohen said, adding that Mr. Weisselberg asked him if he knew anybody who “may have wanted to become a member of one of the golf clubs.” Mr. Cohen ultimately made the payment himself.

In his opening remarks before the House Oversight Committee, Michael Cohen apologized to Congress for previously lying to them and accused President Trump of directing the Moscow Tower negotiations throughout his campaign and lying about it. Photo: Reuters

The Trump Organization finance chief was granted immunity in exchange for testifying before a grand jury last summer in the Manhattan U.S. attorney’s office investigation into Mr. Cohen’s business dealings. That probe has since widened to examine the Trump Organization’s business dealings, according to people familiar with the matter.

Mr. Cohen has made the same account of Mr. Weisselberg’s involvement to federal prosecutors, the Journal reported in November.

Mr. Cohen also offered new details about his efforts to hide the president’s alleged involvement in the hush-money payments last year. Mr. Cohen said he crafted, together with Mr. Trump and Mr. Weisselberg, a statement he issued in February 2018 that said he used his personal funds to pay Ms. Clifford and wasn’t reimbursed by the Trump Organization or the campaign. He said he purposely left Mr. Trump’s name out of the statement. Mr. Trump has denied the sexual encounter.

Mr. Cohen said Mr. Trump told him in a February 2018 call that he wanted Mr. Cohen to express that the president “was not knowledgeable of these reimbursements and he wasn’t knowledgeable of my actions.”

The former Trump lawyer recounted a February 2017 visit to the Oval Office in which Mr. Trump, while giving him a tour, told him, “don’t worry, Michael” and that his reimbursement checks were coming. “They were Fed-Exed from New York and it takes a while for that to get through the White House system,” Mr. Cohen described Mr. Trump as saying.

Michael Cohen told members of Congress that then-candidate Donald Trump knew about WikiLeaks’ plans to release hacked emails in advance. Photo: Getty

The payments to Mr. Cohen were characterized by Mr. Weisselberg as legal fees, but federal prosecutors have said the monthly invoices weren’t connected to any legal services Mr. Cohen provided at that time.

After the 2016 election, Mr. Weisselberg authorized a payment of double what Mr. Cohen had paid Ms. Clifford to cover related income taxes—as well as adding a $60,000 bonus—the Journal has previously reported.

“I have fixed things, but I am no longer your ‘fixer,’ Mr. Trump,” Mr. Cohen said before the committee.

Mr. Cohen also alleged that Mr. Trump knew in advance of WikiLeaks’ plans to release Democratic emails during the 2016 campaign. Mr. Cohen said Roger Stone, an informal adviser to his campaign, told Mr. Trump in a July 2016 phone call that “he had just gotten off the phone with [WikiLeaks founder] Julian Assange and that…within a couple of days, there would be a massive dump of emails that would damage Hillary Clinton’s campaign.”

Mr. Trump’s response, Mr. Cohen said, was “to the effect of ‘wouldn’t that be great.’”

In a hearing before the House Oversight Committee, Michael Cohen described the breaking point that led him to cut ties with President Trump. Photo: Getty

Mr. Stone was charged last month in a seven-count indictment that alleged he told the president’s senior campaign officials as early as June 2016 that he knew WikiLeaks possessed documents damaging to Mrs. Clinton. Mr. Stone pleaded not guilty and has said he had no advance knowledge of the website’s plans.

Mr. Stone said in a text message Wednesday: “Mr. Cohen’s statement is not true.”

Mr. Cohen also made public some private financial statements from 2011 to 2013 that he said Mr. Trump gave to Deutsche Bank AG —a longtime lender to the president—to “inquire about a loan to buy the Buffalo Bills,” according to his opening statement. Mr. Cohen alleged that Mr. Trump at times inflated or deflated his net worth for business and personal purposes, including to avoid paying property taxes. The financial statements were developed by Mr. Trump’s accountant, according to a person familiar with Mr. Cohen’s testimony.

The 2011 and 2012 financial statements each show a net worth between $4 billion and $5 billion. The 2013 statement adds $4 billion in “brand value” and brings the total above $8 billion. Mr. Trump claimed during his presidential campaign to have a net worth exceeding $10 billion. Bloomberg News estimates Mr. Trump’s wealth at $2.84 billion.

A Deutsche Bank spokesman on Wednesday said the bank declined to comment on the financial statements or what role they might have played in the lender’s dealings with Mr. Trump.

The former Trump lawyer’s testimony covered a broad range of alleged misdeeds by the president. He accused the president of committing insurance fraud, saying Mr. Trump inflated estimates of his assets to insurance companies. He alleged that the president hadn’t released his tax returns because he was concerned that would prompt an audit. Mr. Trump has repeatedly said he hasn’t released his tax returns because they were under audit.

Mr. Cohen described racist comments he said Mr. Trump made to him. “He told me that black people would never vote for him because they were too stupid,” Mr. Cohen said. “While we were once driving through a struggling neighborhood in Chicago, he commented that only black people could live that way.”

Mr. Cohen also showed the committee copies of a letter he said he sent at Mr. Trump’s direction threatening the president’s high school, colleges and the College Board not to release his grades or SAT scores.

The hearing delved into the surreal at times. Mr. Cohen testified that American Media Inc., the publisher of the National Enquirer, bought a story about Mr. Trump fathering a love child with a Trump Organization employee, as part of its “catch and kill” approach to buying but not publishing news.

“Is there a love child?” asked Rep. Jackie Speier (D., Calif.).

Newsletter Sign-up Notes on the News Today’s headlines, news in context, and good reads you may have missed, with Tyler Blint-Welsh. PREVIEW

“No, ma’am,” Mr. Cohen said. The story was false, but American Media took it off the market anyway to protect Mr. Trump, he said.

In August Mr. Cohen pleaded guilty to eight federal crimes, including tax evasion and making false statements to a bank. He also implicated the president in two federal crimes when he told prosecutors Mr. Trump directed hush-money payments during the 2016 campaign to Ms. Clifford and former Playboy model Karen McDougal, who alleged she had an affair with Mr. Trump. The president has denied sexual encounters with the two women.

Mr. Cohen also pleaded guilty in November to one count of lying to Congress. He is scheduled to begin a three-year prison term on May 6.

He said Mr. Trump asked him at least six times between January and June of 2016 how the Moscow project was going. Mr. Cohen told Congress in 2017 the project ended in January of the previous year. Mr. Cohen also said he discussed with both Mr. Trump and his campaign manager at the time, Corey Lewandowski, the possibility of sending Mr. Trump to Russia during the campaign as part of the Trump Tower negotiations. Mr. Cohen said Mr. Trump told him to talk to Mr. Lewandowski to “see what dates were available” for him to travel.

Mr. Lewandowski didn’t respond to a request for comment.

Michael Cohen told lawmakers that then-candidate Donald Trump directed him to negotiate a Trump Tower Moscow deal during the 2016 campaign. He also said he previously lied to Congress about the deal to benefit Mr. Trump. Photo: AP

Mr. Cohen said he briefed the president’s children, Ivanka Trump and Mr. Trump Jr.—both executives at the Trump Organization at the time—approximately 10 times about the Trump Tower deal, a statement apparently at odds with 2017 testimony by Mr. Trump Jr. before the Senate Judiciary Committee. Mr. Trump Jr. told the committee that he knew “very little” about the deal and “wasn’t involved.”

Contrary to some media reports, Mr. Cohen said he never was in Prague meeting with Russians before the election. And he said the president didn’t “directly” tell him to lie to Congress in 2017 to play down Mr. Trump’s involvement in efforts during the campaign to build a Trump Tower in Moscow. But in a meeting with Mr. Trump and his lawyer, Jay Sekulow, ahead of his 2017 testimony to a congressional committee, he said Mr. Trump told him: “There is no Russia. There is no collusion. There is no deal.” Mr. Cohen added: “I knew exactly when he wanted me to say.”

On Tuesday morning, Mr. Cohen met behind closed doors with the Senate Intelligence Committee. Mr. Cohen is set to speak before the House Intelligence Committee on Thursday.

Register for WSJ’s Cohen Testimony Conference Call Join WSJ journalists on Feb. 28 as they discuss what Michael Cohen’s House testimony could mean for President Trump. Register here, and send your questions to subscribercall@wsj.com.

—Nicole Hong, Michael Rothfeld and Rebecca Davis O’Brien contributed to this article.

Write to Rebecca Ballhaus at Rebecca.Ballhaus@wsj.com and Joe Palazzolo at joe.palazzolo@wsj.com