Donald Trump has warned that the US will retaliate with “1,000 times greater” force against any Iranian attack on its interests.

Posting on Twitter late on Monday, Trump referred to media reports that Iran was planning retaliation for the assassination by US drone in January of the Iranian general Qassem Suleimani. At the time, analysts predicted Iran would seek to retaliate in the long term.

On Tuesday morning, the president also told Fox & Friends he had wanted to assassinate the president of Syria, Bashar al-Assad, but had been stopped by James Mattis, the retired marine general who was then secretary of defense.

Trump previously denied reports he wanted to assassinate Assad after the Syrian regime carried out chemical weapons attacks on civilians, saying in September 2018 it was “never even discussed”.

Suleimani was killed in a drone strike on 3 January, after Trump was impeached but before his Senate trial. Critics said the strike was meant as a distraction. Suspicions about Trump’s motives were fueled by the White House’s changing account of the underlying intelligence.

The secretary of state, Mike Pompeo, at first said the assassination was “in response to imminent threats to American lives”, but in the following weeks Trump officials walked back the assertion they were acting on a specific threat.

On Sunday, a Politico story citing unnamed intelligence officials said Iran was plotting to kill the US ambassador to South Africa, Lana Marks, a handbag designer and longtime Trump friend. She was placed under extra security protection.

“According to press reports, Iran may be planning an assassination, or other attack, against the United States in retaliation for the killing of terrorist leader Soleimani,” Trump tweeted on Monday night.

“Any attack by Iran, in any form, against the United States will be met with an attack on Iran that will be 1,000 times greater in magnitude!”

The next morning, Trump repeated his threat in an interview with Fox & Friends, saying: “We’re all set and if they do anything to anybody they’ll be hit 1,000 times harder than they hit us.”

He also discussed the plan to assassinate Assad.

“I had a shot to take him out if I wanted and Mattis was against it,” Trump said. “Mattis was against most of that stuff … he didn’t know how to win.”

Trump originally denied wanting to have Assad killed after the story was included in Fear, the first book about his administration by Bob Woodward.

The veteran Washington Post reporter detailed a call to Mattis in which he quoted Trump as saying: “Let’s fucking kill him! Let’s go in. Let’s kill the fucking lot of them.”

Mattis features heavily in Rage, Woodward’s new Trump book. The veteran of Watergate details the general’s attempts to contain Trump, his growing disillusionment – including offering prayers for the country at the national cathedral in Washington – and his ultimate resignation.

Told by Fox & Friends the decorated general was “a great American” who “gave a lot to the country”, Trump said: “I don’t say he’s a good American or bad American. I just say he didn’t do a good job. I let him go.”

Rage also sheds new light on Trump’s decision to assassinate Suleimani. In Woodward’s telling, Trump worked through the decision over a round of golf with the South Carolina senator Lindsey Graham, a Republican foreign policy hawk.

“I’m thinking of hitting Suleimani,” Trump is quoted by Woodward as saying.

“Oh, boy, that’s a giant step!” Graham is quoted as replying. In Woodward’s account, Trump said: “We have all these intercepts showing that Suleimani is planning attacks.”

“Yeah, he’s always been doing that,” Graham reportedly replied.

The then White House chief of staff, Mick Mulvaney, is depicted as “almost begging” Graham to find a way to stop Trump carrying out his plan, which Graham reportedly told Trump was “over the top”. On Monday, Mulvaney told Fox Business he had “absolutely no regrets about how the president handled that situation”.

In spite of his saber-rattling on Twitter and Fox News, at a White House ceremony on Tuesday to mark normalization agreements between Israel and the United Arab Emirates and Bahrain, Trump said he would make a deal with Iran.

“I’m going to make a great deal with Iran … I will help them in any way possible,” he said. “But they should wait until after the election,” he explained, because his opponent Joe Biden “would be a dream” for Tehran.

Trump’s public explanations for the Suleimani assassination at the time were much more dramatic than what Woodward reports he told Graham.

“We did it because they were looking to blow up our embassy,” Trump said at a 9 January news conference.

But the same day Pompeo contradicted him, saying, “There were a series of imminent attacks that were being plotted by Qassem Suleimani. We don’t know precisely when and we don’t know precisely where.”

The next day Trump said, “I think it would have been four embassies. Could have been military bases, could have been a lot of other things too.

“But it was imminent.”