Donald Trump sought to regain his footing after a torrid week with a fiery speech using two of his favourite tactics: going off script and hurling insults at opponents.

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Basking in adulation at the Conservative Political Action Conference (CPAC), the president said: “You know I’m totally off script right now and this is how I got elected, by being off script. And if we don’t go off script, our country’s in big trouble, folks, because we have to get it back.”

In a rambling speech that lasted for two hours, he took aim at a Democratic proposal to tackle climate change by adopting a sweeping “Green New Deal”, attacked by Republicans as expensive and bound to curtail cars and planes. Trump said sarcastically: “I think the new green deal, or whatever the hell they call it. The Green New Deal, right? I encourage it. I think it’s really something that they should promote.”

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To laughter, Trump continued, mockingly: “No planes. No energy. When the wind stops blowing, that’s the end of your electric. ‘Let’s hurry up. Darling, darling, is the wind blowing today? I’d like to watch television, darling.’”

The crowd erupted in cheers and applause.

Trump also insisted he had been joking when, at a press conference in July 2016, he encouraged Russia to find his rival Hillary Clinton’s missing 30,000 emails, and blamed the “sick” media for using it to incriminate him. The audience chanted: “Lock her up! Lock her up!” – a common anti-Clinton refrain.

The president described the justice department’s Russia investigation as “a phoney witch-hunt” and claimed that since no collusion has yet come to light, Democrats in the House now want to look into his personal finances. He dismissed such oversight efforts with an unpresidential word: “Bullshit.”

Trump went on to rail against James Comey, whom he fired as FBI director, and Jeff Sessions, his former attorney general, even mocking the latter’s southern accent.

He also made false claims about everything from the unemployment rate to the crowd size at his inauguration. He insisted a wall on the US-Mexico would be built, prompting more cries of “USA! USA!”

He then went on to make remarks that some interpreted as an inflammatory attack on foreign-born members of Congress.

“Right now we have people in Congress that hate our country and you know that,” he said. “And we can name every one of ’em if they want. They hate our country. Sad. It’s very sad. When I see some of the things being made, the statements being made, it’s very, very sad.

“And find out, how did they do in their country? Just ask ’em, how did they do? Did they do well, were they succeeding? Just ask that question. Somebody would say, ‘Oh, that’s terrible that he brings that up.’ But that’s OK, I don’t mind, I’ll bring it up. How did they do in their country? Not so good, not so good.”

He also accused Democrats of “embracing socialism”, including a radical plan for healthcare he said would lead to “colossal tax increases”. Trump invited a conservative student from California onstage and said he would soon be signing an executive order requiring colleges and universities to protect free speech.

A shot of hero worship was just what the doctor ordered. It has become a commonplace in Washington to ponder what qualifies as “Trump’s worst week”, but the past seven days are clearly a contender. Domestically, there was damning testimony from his former lawyer and fixer Michael Cohen. Internationally, there was a much-hyped summit with North Korea that collapsed in failure and controversy.

Larry Jacobs, director of the Center for the Study of Politics and Governance at the University of Minnesota, said: “In a lot of ways, Trump has been a magician in masterminding a narrative that he’s going to stand up for America and he’s not beholden to the swamp. This week put the lie to Trump’s narrative.

“The collapse of the talks in North Korea has put the lie to his story that he had a historic accomplishment. It became clear there has not been a breakthrough and Trump conceded the point and left. Back home, the idea Trump is a beacon of truth was seriously damaged by what Michael Cohen said and the people he identified who will be brought forward to testify.”

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Cohen, who once said he would “take a bullet” for Trump, branded his former boss a cheat, conman and racist and accused him of breaking the law in office. He alleged Trump lied about business dealings in Russia during the 2016 election and ordered him to conceal extramarital relationships. And he likened Trump to a “mobster” who demanded blind loyalty from staff and expected them to lie and threaten adversaries on his behalf.

On Friday, the president let rip with a series of tweets attacking his former lawyer, who pleaded guilty last year to lying to Congress and reports to prison soon for a three-year sentence.

But Cohen has thrown open floodgates for Congress to interview further Trump allies and associates, possibly including his son Don Jr and daughter Ivanka. House investigators will hear from Felix Sater, a Russia-born executive who worked with Cohen on an ultimately unsuccessful deal to build a Trump Tower in Moscow, in an open hearing on 14 March.

Jacobs added: “I don’t think I’ve seen anything so devastating to a president since Richard Nixon. Put simply, it only gets worse for Trump in the investigations. It’s going to be months of searing testimony for him, his election and indeed his business.”

Piling on the domestic pressure, the New York Times reported that Trump ordered his former chief of staff to grant Jared Kushner, his son-in-law and senior adviser, top-level security clearance against the guidance of intelligence officials. Democrats have demanded the White House turn over relevant documents.

Facebook Twitter Pinterest Donald Trump arrives to speak at Conservative Political Action Conference. Photograph: Carolyn Kaster/AP

Some 8,300 miles away, Trump’s second meeting with the North Korean dictator, Kim Jong-un, ended abruptly amid disagreement over the extent of sanctions relief Pyongyang would get in exchange for steps to give up its nuclear weapons.

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“Sometimes you have to walk,” the self-proclaimed deal-maker reasoned, but the stalemate raised fresh questions over Trump’s improvisational approach to diplomacy, and sowed doubts over whether North Korea will ever fully denuclearise.

The cloud had a silver lining – “no deal is better than a bad deal” was a widely expressed verdict – but it soon darkened as Trump praised Kim’s leadership and took him at his word that he had not been aware of how Otto Warmbier, an American student who died after 17 months in a North Korean prison, had been treated.

The House intelligence committee chairman, Adam Schiff, called the comments “detestable”. On Friday, Warmbier’s parents blamed Kim’s “evil regime” for his death and said: “No excuse of lavish praise can change that.”

Trump claimed on Twitter he had been “misinterpreted”, but critics noted that he has been similarly willing to accept the word of autocrats in Russia and Saudi Arabia.

It was, by any measure, another bruising week. But associates of Trump sought to play down its long-term significance.

Chris Ruddy, chief executive of conservative Newsmax Media, told Reuters: “There were no surprises this week. We knew North Korea was a tough nut to crack and that Michael Cohen was going to say a lot of nasty stuff. At the end of the day I don’t think it changes the political climate for President Trump.”