Trump said Iran had offered not to possess nuclear weapons for more than 20 years. Tehran's nuclear ambitions were a sticking point at talks in Islamabad last weekend.
"We're going to see what happens. But I think we're very close to making a deal with Iran," he told reporters outside the White House o Thursday.
Hours later at an event in Las Vegas, Nevada, Trump went further, saying the war "should be ending pretty soon".
Trump said he was not sure a two-week ceasefire agreed with Iran last week would need to be extended beyond next week, and added Tehran wanted to make a deal.
"We have a very good relationship with Iran right now, as hard as it is to believe. And I think it's a combination of about four weeks of bombing, and a very powerful blockade," he said.
At last weekend's talks, the US proposed a 20-year suspension of all nuclear activity by Iran - an apparent concession from longstanding demands for a permanent ban. Tehran suggested a halt of three to five years, according to people familiar with the proposals.
Washington has pressed for any highly enriched uranium (HEU) to be removed from Iran. Tehran has demanded that international sanctions against it be lifted.
Trump said he had held "excellent conversations" with Israeli Prime Minister Benjamin Netanyahu and Lebanese President Joseph Aoun and planned to invite them both to the White House for "meaningful talks".
He said later that the White House meeting could take place over the next week or two, and that if an Iran deal was reached and signed in Islamabad, he might go for that.
Trump said he had directed US Vice President JD Vance, Secretary of State Marco Rubio and Chairman of the Joint Chiefs of Staff Dan Caine to work with Israel and Lebanon to achieve lasting peace.
The war with Iran spilt into Lebanon on March 2, when Hezbollah opened fire in support of Tehran, prompting an Israeli offensive in Lebanon 15 months after the last major conflict.
Thousands of people have been killed, mostly in Iran and Lebanon, since US-Israeli attacks on Iran began on February 28, triggering Iranian airstrikes on Iran's Gulf neighbours and renewed fighting between Israel and Hezbollah.
Closure of the Strait of Hormuz has caused the worst oil price shock in history and forced the International Monetary Fund to downgrade its outlook for the global economy, warning prolonged conflict could push the world to the brink of recession.
US Defence Secretary Pete Hegseth said troops were poised to restart combat operations if a deal was not reached.
A Pakistani security source told Reuters Washington was offering to lift sanctions and unfreeze billions of dollars' worth of Iranian assets to secure a deal.
However, the source added that Iran would open the strait only if a permanent ceasefire is reached and there are United Nations guarantees the US and Israel will not attack again in future.
"We hope that the field marshal will have a draft in his hand when he flies out of Tehran," the source said.
