The White House rebutted a published report Tuesday alleging that President Trump asked then-FBI Director James B. Comey in February to shut down an investigation of the president’s former national security adviser, Michael Flynn.

“While the president has repeatedly expressed his view that General Flynn is a decent man who served and protected our country, the president has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving General Flynn,” a senior White House official said in a statement.

The New York Times, citing a memo written by Mr. Comey, said the president asked the FBI director during an Oval Office meeting on Feb. 14 to kill the Flynn investigation.

“I hope you can see your way clear to letting this go, to letting Flynn go,” Mr. Trump told Mr. Comey, according to the memo cited by The Times. “He is a good guy. I hope you can let this go.”

Mr. Trump told Mr. Comey that Mr. Flynn had done nothing wrong, according to the memo.

The report touched off a new round of calls among congressional Democrats for an independent investigation of the president, with some saying Mr. Trump may have obstructed justice and could merit impeachment proceedings.

Some Republicans also said they want Mr. Comey to turn over the memo and testify to Congress.

“On a day when we thought things couldn’t get worse, they have,” said Sen. Charles E. Schumer, New York Democrat. “The country is being tested in unprecedented ways.”

Rep. Elijah E. Cummings, Maryland Democrat, said on CNN of the president, “Now he’s stepped over the line. I think it’s a sad day for our country.”

The White House scrambled to push back against the latest crisis, just a day after the president and his advisers tried to contain the political fallout from a published report that Mr. Trump had provided classified intelligence to Russian officials about the Islamic State.

“The president has the utmost respect for our law enforcement agencies and all investigations,” the White House official said of the Comey memo. “This [report] is not a truthful or accurate portrayal of the conversation between the president and Mr. Comey.”

The accusation about the president comes a week after Mr. Trump fired Mr. Comey. The president called Mr. Comey a “showboat” and said he wasn’t satisfied with his job performance on the Hillary Clinton email investigation last year. Mr. Trump also cited the FBI investigation of his campaign’s alleged ties to Russia, saying in an interview he thought the allegations were phony but also saying he wasn’t trying to impede the probe.

The White House also noted that acting FBI Director Andrew McCabe told Congress last week that the White House had not interfered with any investigations.

“There has been no effort to impede our investigation to date,” Mr. McCabe said. “Simply put, you cannot stop the men and women of the FBI from doing the right thing.”

The acting director, who took over after Mr. Comey was fired, also testified last week that the FBI was confident it had secured Mr. Comey’s files and electronic devices to preserve information about ongoing investigations.

The meeting between Mr. Trump and Mr. Comey came one day after the president fired Mr. Flynn for misleading Vice President Mike Pence about the extent of his conversations with the Russian ambassador to the U.S. during the presidential transition.

A federal grand jury in Virginia has issued subpoenas for records related to Mr. Flynn. The Flynn probe reportedly is examining, in part, his financial ties to Russia and Turkey. The existence of the Comey memo was confirmed by several news organizations.

Rep. Adam B. Schiff of California, ranking Democrat on the House Intelligence Committee, said he wants to bring Mr. Comey to Congress to testify on the Flynn matter and his conversations with the president about the FBI’s Russia investigation.

He also said Congress should review Mr. Comey’s written notes about meetings with the president.

“Enough is enough. Congress really needs to get to the bottom of this,” Mr. Schiff told reporters.

At least two Republicans spoke similarly. Rep. Jason Chaffetz of Utah said on Twitter that his Oversight Committee “is going to get the Comey memo, if it exists. I need to see it sooner rather than later. I have my subpoena pen ready.”

And Sen. Lindsey Graham of South Carolina said he is “not going to take a memo, I want the guy to come in” and testify.

Senators reporting for evening votes Tuesday faced a bout of deja vu, as reporters descended on them to get reaction to yet another bombshell news report.

“You’re watching an obstruction of justice investigation developing in real time,” said Sen. Richard Blumenthal, Connecticut Democrat. “If there were any question about the need for an independent special prosecutor, this report is the nail on the argument.”

He said any tapes, transcripts or memos related to the recent controversies must be preserved in case there are legal proceedings in the future.

“I think this is all so outrageous,” said Rep. James P. McGovern, Massachusetts Democrat. “I think with each passing day, this president proves to Americans that he doesn’t have the temperament, he doesn’t have the qualifications, he doesn’t have the skill to lead this nation. His erratic behavior, his bizarre behavior — it’s really scary.”

• Stephen Dinan, Tom Howell Jr. and Andrea Noble contributed to this report.

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