US President Donald Trump has reiterated his readiness to meet his Iranian counterpart Hassan Rouhani, while Tehran reiterates its rejection of any negotiations with Washington before the sanctions are lifted.

Speaking at the White House, Trump said that meeting with his Iranian counterpart is out of the question and is in Tehran's interest.

"I have no problem holding a meeting," he said. "Iran has to be upright because it is in a very bad situation right now. They have to fix their situation.

The US president hinted last Wednesday on the possibility of holding a meeting with Rouhani during the upcoming meetings of the United Nations General Assembly in New York scheduled for later this month.

"Everything is possible," Trump told reporters at the White House when asked about a possible meeting with Rouhani at those meetings.

However, Rouhani says his country will not hold talks with the United States unless Washington lifts all sanctions it re-imposed on Tehran after the withdrawal from the nuclear deal.

The US special envoy to Iran, Brian Hook, said last week that more sanctions would be imposed on Iran and that the United States was committed to campaigning extreme pressure on Tehran.

In May 2018, Washington withdrew from the nuclear deal with Iran, saying it was insufficient to curb Tehran's ambitions, and imposed new tough sanctions.

That prompted Tehran - a year after the US move - to scale back its obligations under the deal, which restricts its nuclear program in exchange for lifting Western sanctions.

The European Union is working hard to prevent the deal from collapsing altogether and says it is the best way to prevent Iran from developing a nuclear weapon.