The United States has been told it will need to rejoin the Iran nuclear deal to realize President Donald Trump's proposal on Monday for a one-to-one talk with his Iranian counterpart Hassan Rouhani.

During a joint news conference with visiting Italian Prime Minister Giuseppe Conte, Trump said he "will meet with anybody" and a meeting between the US and Iranian leaders is good for both sides and the world.

However, Rouhani's adviser Hamid Aboutalebi said on Tuesday that any talks with the US had to start with reducing hostility and a return to the nuclear deal.

"Respect for the great nation of Iran, reduction in hostilities, US returning to the nuclear deal.... That will open the rocky path of the moment," he wrote on Twitter.

Iranian Supreme Leader Ayatollah Ali Khamenei said late on Monday that any negotiation with the US to solve the existing problems is an "obvious mistake".

"I have reiterated that we cannot rely on the US words and even their signature, therefore, negotiations with them are fruitless," he said.

The Iranians rejected eight requests from Trump for one-on-one talks last year, Rouhani's Chief of Staff, Mahmoud Vaezi, said earlier this month in an Iranian newspaper.

Ma Xiaolin, a professor from Beijing Foreign Studies University, said Rouhani may not want to sit down with Trump unless Washington comes back to the nuclear deal, also known as the Joint Comprehensive Plan of Action, or JCPOA.

It was signed in 2015 by Iran, China, France, Russia, the United Kingdom, the US, Germany and the European Union. The US withdrew from the deal in May and reimposed sanctions against Iran.

Ma said Teheran knows that Trump wants Iran to completely abandon its nuclear weapons and ballistic missiles, as well as its status in the Middle East.

"It is quite impossible for both sides to meet if there are still additional sanctions against Iran," he said, adding that Iran has made its compromise by accepting a series of restrictions in the deal, and a situation of mutual trust between Teheran and Washington is a prerequisite for potential talks.

The meeting, as Trump described, has no preconditions. "No preconditions, no. If they want to meet, I'll meet, anytime they want, anytime they want," he said.

US Secretary of State Mike Pompeo, however, added several qualifications to the president's invitation on Monday.

"If the Iranians demonstrate a commitment to make fundamental changes in how they treat their own people, reduce their malign behavior, can agree that it's worthwhile to enter in a nuclear agreement that actually prevents proliferation, then the president said he's prepared to sit down and have a conversation with him," he said.

Pan Jie and Xinhua contributed to this story.