By Nayera Abdallah, Parisa Hafezi and Tala Ramadan

DUBAI (Reuters) -U.S. President Donald Trump said on Thursday that the United States was getting very close to securing a nuclear deal with Iran, and Tehran had "sort of" agreed to the terms.

"We're in very serious negotiations with Iran for long-term peace," Trump said on a tour of the Gulf, according to a shared pool report by AFP.

"We're getting close to maybe doing a deal without having to do this... there (are) two steps to doing this, there is a very, very nice step and there is the violent step, but I don't want to do it the second way," he said.

An Iranian source familiar with the negotiations said there were still gaps to bridge in the talks with the United States.

Oil prices fell by about $2 on Thursday on expectations for a U.S.-Iran nuclear deal that could result in sanctions easing.

Talks between Iranian and U.S. negotiators to resolve disputes over Tehran's nuclear programme ended in Oman on Sunday with further negotiations planned, officials said, as Tehran publicly insisted on continuing its uranium enrichment.

The Trump administration gave Iran a proposal for a nuclear deal during the fourth round of negotiations on Sunday, a U.S. official and two other sources with direct knowledge of the matter told Axios.

Though Tehran and Washington have both said they prefer diplomacy to resolve the decades-long nuclear dispute, they remain divided on several red lines that negotiators will have to circumvent to reach a new deal and avert future military action.

Iran's president reacted to Trump's comments on Tuesday in which he called Tehran the “most destructive force” in the Middle East.

“Trump thinks he can sanction and threaten us and then talk of human rights. All the crimes and regional instability is caused by them (the United States),” Masoud Pezeshkian said.

“He wants to create instability inside Iran.”

However, in an interview with NBC News published on Wednesday, an Iranian official said Iran was willing to agree to a deal with the U.S. in exchange for the lifting of economic sanctions.

Ali Shamkhani, an adviser to Iran's Supreme Leader Ayatollah Ali Khamenei, said Iran would commit to never making nuclear weapons and getting rid of its stockpiles of highly enriched uranium, agree to enrich uranium only to the lower levels needed for civilian use and allow international inspectors to supervise the process, NBC reported.

'RED LINE'

U.S. officials have publicly stated that Iran should halt uranium enrichment, a stance Iranian officials have called a "red line" asserting they will not give up what they view as their right to enrich uranium on Iranian soil.

However, they have indicated a willingness to reduce the level of enrichment.

Iranian officials have also expressed readiness to reduce the amount of highly enriched uranium in storage—uranium enriched beyond the levels typically needed for civilian purposes, such as nuclear power generation.

But they have said it would not accept lower stockpiles than the amount agreed in a deal with world powers in 2015 - the deal Trump quit.

The Iranian source said that while Iran is prepared to offer what it considers concessions, "the issue is that America is not willing to lift major sanctions in exchange."

Western sanctions have severely impacted the Iranian economy.

Regarding the reduction of enriched uranium in storage, the source noted: “Tehran also wants it removed in several stages, which America doesn't agree with either.”

There is also disagreement over the destination to which the highly enriched uranium would be sent, the source added.

(Reporting By Nayera Abdallah and Tala Ramadan; Writing by Michael Georgy; Editing by Ros Russell)