Donald Trump has challenged his secretary of state to “compare IQ tests”, if Rex Tillerson did call the president a “moron” as reported.

Trump told Forbes magazine: “I think it’s fake news. But if he did [say] that, I guess we’ll have to compare IQ tests. And I can tell you who is going to win.”

The president spoke to the magazine on Friday and the interview was published online on Tuesday. Last week, an NBC story claimed Mike Pence, the vice-president, had to talk Tillerson out of resigning this summer, and that Tillerson had called Trump a “moron”. Some reports said he called the president “a fucking moron”.

Tillerson said he never considered resigning but did not deny calling Trump a moron. His spokeswoman said he never used such language.

In brief comments to reporters in the Oval Office hours after Trump’s comments to Forbes were published and ahead of a meeting with Henry Kissinger, the president was asked if he had undercut Tillerson by questioning his IQ.

“No, I didn’t undercut anybody,” he said. “I don’t believe in undercutting people.”

Later, at the daily White House briefing, the press secretary, Sarah Sanders, insisted: “The president never implied the secretary of state was not incredibly intelligent. He made a joke – nothing more than that. He has full confidence in the secretary of state … They’re working hand in hand to move the president’s agenda forward.”

She chided reporters: “Maybe you guys should get a sense of humor and try it some time … He’s got 100% confidence in the secretary of state. We’re trying to move forward and talk about the agenda whereas you guys are trying to talk about who likes who.”

Speaking to Forbes, Trump also claimed to have had “just about the most legislation passed of any president, in a nine-month period, that’s ever served. We had over 50 bills passed. I’m not talking about executive orders only, which are very important. I’m talking about bills.”

Trump has made such claims of unprecedented legislative success before – and had them debunked. He added: “I also have another bill … an economic development bill, which I think will be fantastic. Which nobody knows about. Which you are hearing about for the first time.”

Under that bill, he said, companies that kept jobs in America would be rewarded while those sending operations offshore would “get penalized severely”.

“It’s both a carrot and a stick,” Trump said. “It is an incentive to stay. But it is perhaps even more so – if you leave, it’s going to be very tough for you to think that you’re going to be able to sell your product back into our country.”

In a volley of four tweets issued on Tuesday morning, meanwhile, Trump seemed to say he was about to issue an executive action on healthcare. “Since Congress can’t get its act together on HealthCare,” he wrote, “I will be using the power of the pen to give great HealthCare to many people – FAST.”

Republican attempts to repeal and replace the Affordable Care Act (ACA) have repeatedly failed in the Senate amid widespread opposition to plans that, nonpartisan analysis has said, would take access to health insurance away from millions of Americans.

Trump’s threat of executive action – he has said he may sign an order to allow people to buy insurance across state lines – stood at odds with what he told Forbes. “The Democrats want to make a deal,” he said. “At the same time, I think I have a deal with the Republicans. So I have the best of both worlds. That’s business to a certain extent. I’m very able to make deals with Democrats if I have to.”

Members of the president’s own party have voted down the ACA replacement plans and one deficit hawk, Bob Corker of Tennessee, has emerged as an establishment voice against planned tax reform. Over the weekend, Trump and Corker engaged in a bizarre exchange of insults on Twitter and, in Corker’s case, through the pages of the New York Times.

“The failing New York Times set Liddle’ Bob Corker up by recording his conversation,” Trump tweeted on Tuesday, coining a new nickname based on Corker’s height (5ft 7in) and accusing the newspaper of malpractice. “[Corker] was made to sound a fool, and that’s what I am dealing with!”

On Sunday one of the Times reporters, Jonathan Martin, tweeted that Corker had planned his attack. “He had two aides on line, one taping us,” Martin wrote. “Corker is effectively staging a slow-rolling public intervention with Trump.”

Sanders joined the fray on Tuesday, telling reporters: “Senator Corker is entitled to his own opinion but he’s certainly not entitled to his own facts.”

She also elaborated on Trump’s claim that Corker is responsible for the Iran nuclear deal, which the president has fiercely criticised. “Senator Corker worked with Nancy Pelosi and the Obama administration to pave the way for that legislation and basically rolled out the red carpet for the Iran deal,” she said.

Sanders was challenged over the claim as reporters noted that Corker had opposed the deal. But she dug in, saying: “He worked with them on the legislation that rolled that out. That’s what helped I think put things in motion. He may have voted against the deal ultimately, but he not only allowed the deal to happen, he gave it credibility. I stand by my statement.”

Asked if Corker should resign, as Trump’s former chief strategist Steve Bannon has demanded, Sanders replied: “I think that’s a decision for Senator Corker and the people of Tennessee, not for us to decide.”

Also on Twitter on Tuesday, Trump turned his fire on Democrats over the possibility of a deal to protect Dreamers, young undocumented migrants brought to the country as children and previously protected by the Obama administration.

Democratic leaders expressed strong opposition to a list of hardline demands the White House issued on Sunday. Among other measures, the White House said funding for a border wall with Mexico would be part of any accord. Democrats and Dreamers reacted with horror; the Congressional Hispanic Caucus said no deal could proceed if a wall was included.

“The problem with agreeing to a policy on immigration is that the Democrats don’t want secure borders,” Trump wrote on Tuesday. “They don’t care about safety for USA.”

Trump also complained again about the NFL, in which player protests during the anthem continue. “Why is the NFL getting massive tax breaks while at the same time disrespecting our anthem, flag and country?” he wrote. “Change tax law!”

The NFL gave up its federal tax-exempt status a few years ago and files tax returns as a taxable entity.

The final tweet of the early morning sequence took aim at ESPN and an anchor suspended over the anthem controversy. The tweet also returned to one of Trump’s main preoccupations: ratings.