Donald Trump has said his former attorney Michael Cohen lied when he testified that Trump directed him to break the law.

In a freewheeling interview with the Associated Press, the president also:

criticised global condemnation of Saudi Arabia over the disappearance and reported death of reporter Jamal Khashoggi

said he would pursue trade deals with Japan, Britain and the European Union

confirmed that Pat Cipollone will be his new White House counsel

said he could fire attorney general Jeff Sessions “whenever I want to”

and said he will not accept the blame if Republicans lose the House in November.

In an interview with Fox News, Trump also renewed his criticism of the Federal Reserve.

Cohen pleaded guilty in August to campaign finance charges which alleged he coordinated with Trump to buy the silence of an adult film star and a Playboy model who allege affairs that Trump denies.

On Tuesday, he said that claim was “totally false”. He also dismissed Cohen – who worked for him for years as a personal attorney and who once said he would “take a bullet” for his boss – as “a PR person who did small legal work”.

A day after a defamation lawsuit brought by the adult film star, Stormy Daniels, was thrown out of court, Trump declined an opportunity to apologise for calling her “Horseface” in a tweet.

“You can take it any way you want,” he said.

Prosecutors signaled that they accepted Cohen’s account of what occurred. Trump nonetheless derided Cohen and said it was “very sad” he had struck a deal to “achieve a lighter sentence”.

Last week, Cohen’s lawyer said Trump’s former fixer had changed his political registration from Republican to Democrat, in an attempt to distance “himself from the values of the current” administration before the midterm elections.

Trump is not on the ballot on 6 November but he told the AP he believes he is “helping” Republican candidates as he stages large rallies in favourable states. Most analysts predict the Democrats will retake the House but the president said he thought the GOP was “going to do well” in an election that “feels to me very much like” 2016.

Of his efforts on the campaign trail, Trump said: “I don’t believe anybody has ever had this kind of impact.” He resisted comparisons to Barack Obama, who took responsibility for the Democrats’ defeat in 2010, when they lost the House, by acknowledging that his party got “shellacked”.

If Democrats take the House and pursue impeachment or investigations including seeking his tax returns, Trump said he would “handle it very well”.

The appointment of Cipollone, a commercial litigator based in Washington, has been widely reported. As White House counsel, he would bear the brunt of any congressional subpoenas and investigations. Trump said he was “a great guy” and “very talented”.

Here we go again with, you know, you’re guilty until proven innocent. I don’t like that Trump on the Khashoggi case

Cipollone’s predecessor, Don McGahn, has attempted to steer Trump through special counsel Robert Mueller’s investigation of Russian election interference, links between Trump aides and Moscow and potential obstruction of justice by the president. He announced his departure last month, saying he would leave after the appointment of Brett Kavanaugh to the supreme court.

Trump’s frustration with another legal official, attorney general Jeff Sessions, remains strong, over how Sessions has handled the Russia investigation. He told the AP: “I can fire him whenever I want to fire him.”

He also said he hoped to announce a replacement for United Nations ambassador Nikki Haley in the next week or two. Haley announced her departure last week, leading to speculation Trump could appoint his own daughter, Ivanka Trump, to replace her.

Asked about the case of Khashoggi, who Turkish officials have said was murdered in the Saudis’ Istanbul consulate, Trump compared it to allegations of sexual assault leveled against Kavanaugh during his confirmation hearing.

“I think we have to find out what happened first,” Trump said. “Here we go again with, you know, you’re guilty until proven innocent. I don’t like that. We just went through that with justice Kavanaugh and he was innocent all the way as far as I’m concerned.”

On trade, the Trump administration notified Congress on Tuesday it will pursue agreements with the European Union, Japan and Britain. Under US law, that means talks can formally begin after at least 30 days.

Philip Levy, senior fellow at the Chicago Council on Global Affairs, told the AP each of the three negotiations would pose problems. French president Emmanuel Macron has said he will not support EU talks with any country not part of the Paris climate change pact. Trump withdrew the US from the agreement last year.

Talks with Britain cannot begin as long as it is still part of the EU, while Japan only agreed to talks as a way to stave off tariffs Trump has threatened to impose on cars.

Regarding the Federal Reserve, Trump told Fox News it was his “biggest threat” because it was raising interest rates too quickly.

The president said he did not speak with Fed chair Jerome Powell because of the Fed’s political independence but said: “I’m not happy with what he’s doing because it’s going too fast.”

Asked about his decision to replace Obama-appointee Janet Yellen with Powell, Trump said: “Can I be honest? I’m not blaming anybody. I put him there and maybe it’s right, maybe it’s wrong but I put him there.”

Last week, Trump called the Fed “out of control”, though he said he would not seek to oust Powell. Those remarks came as the stock market, which Trump has often cited as a barometer for his stewardship of the US economy, was plunging. Trump blamed the turmoil on the Fed’s rate hikes.