Two of Donald Trump's top lieutenants said on Tuesday he is ready to meet his Iranian counterpart without preconditions after the US president sacked his hawkish national security adviser, while insisting there will be no easing of pressure on Tehran.

Even as the removal of national security hardliner John Bolton triggered speculation that Trump might soften his approach to Iran, Secretary of State Mike Pompeo joined Israel in alleging "possible undeclared nuclear activities" by Tehran, and the US administration imposed new terrorist designations on leaders of some groups linked to the Islamic republic.

Amid the fraught political climate, Trump loyalists signalled he is prepared to meet with Iranian President Hassan Rouhani — something that French President Emmanuel Macron had proposed in an effort to salvage a 2015 nuclear accord with Tehran from which Trump withdrew the United States.

"Now the president has made clear, he is happy to take a meeting with no preconditions, but we are maintaining the maximum pressure campaign," Treasury Secretary Steven Mnuchin said, just days after Iran announced it had fired up centrifuges to boost its enriched uranium stockpiles.

Pompeo, standing alongside Mnuchin in the White House, said "sure" when asked whether Trump could meet Rouhani later this month at the United Nations General Assembly in New York.

The remarks came just 90 minutes after Trump announced he had sent Bolton packing, and Pompeo and Mnuchin cautioned that Bolton's exit should not be seen as heralding major policy shifts.

"I would say Secretary Pompeo and myself and the president are completely aligned on our maximum pressure campaign," Mnuchin said.

Tehran reacted swiftly to Bolton's departure, with a Rouhani aide saying it signaled Washington's pressure was failing.

"Bolton's marginalization and his subsequent removal isn't an accident but a clear sign of the defeat of America's maximum pressure strategy" against Iran, Hesameddin Ashena tweeted.

"Have no doubt that we have the power to manage the US approach towards Iran and will never back down. The blockade of Iran will break."

Going 'soft?'

If Tehran sees optimism in Bolton's ouster, some hawkish US lawmakers warned that easing the squeeze on Iran would be an enormous mistake, enabling Europe to, in Senator Ted Cruz's words, "send an economic lifeline to the Ayatollah."

Cruz tweeted that he hoped Bolton's departure "does not mean that the deep-state forces at State and Treasury — who have been fighting tooth and nail to preserve the Obama Iran nuclear deal — have finally convinced the president to go soft on Iran."

Meanwhile, the Trump administration announced new terrorist designations against leaders or operatives of organisations with close ties to Tehran, among them Iran's Islamic Revolutionary Guard Corps-Qods Force and Hezbollah.

The US also designated leaders of groups within the Islamic State and Al-Qaeda, and the operational arm of Hamas.

"You know we've done more sanctions on Iran than anybody, and it's absolutely working," Mnuchin said.

Tensions have been escalating between Iran and the United States since May last year, when Trump pulled out of the 2015 nuclear accord with Tehran and began reimposing sanctions that have crippled the Iranian economy.

On Tuesday, Washington joined Israel in accusing Iran of new deceptions about its nuclear program, a move that further strained European-led attempts to salvage a multinational deal.

Iran denounced the accusations levelled on Monday by Israeli Prime Minister Benjamin Netanyahu, who said that the clerical regime operated a previously undisclosed site aimed at developing nuclear weapons but destroyed it after it was detected.

Pompeo, without directly referencing Netanyahu, urged Iran to comply with the UN nuclear watchdog, the International Atomic Energy Agency.

"The Iranian regime's lack of full cooperation with @iaeaorg raises questions about possible undeclared nuclear material or activities," Pompeo tweeted.

"The world won't fall for it. We will deny the regime all paths to a nuclear weapon."

A potential summit between Trump and the Iranian leadership sparked interest from the mogul-turned-president, but it is adamantly opposed by Netanyahu, who faces elections next week and sees Iran as an existential threat.

In a live television address, Netanyahu showed pictures of an alleged site near Abadeh, south of Isfahan, where he said Iran conducted experiments to develop nuclear weapons.

Netanyahu said Israel found out about the site during a daring raid into Tehran and that the regime demolished the site sometime between late June and late July after realizing that Israel was aware.