Amid a massive US military build-up in the Middle East that has fuelled fears of a wider war, Trump said negotiations with Iran were going well but insisted Tehran has to reach a "meaningful" agreement.
"Otherwise bad things happen," Trump, who has repeatedly threatened to attack Iran, told the first meeting of his Board of Peace in Washington.
Trump spoke of the US airstrikes carried out in June, saying Iran's nuclear potential had been "decimated", adding "we may have to take it a step further or we may not".
"You'll be finding out over the next probably 10 days," he said. Asked later to elaborate, he told reporters aboard Air Force One: "I would think that would be enough time, 10, 15 days, pretty much maximum."
But he declined to be specific, except to warn again of "really bad things" and insist that Iran would have to make a deal one way or another.
US threats to bomb Iran, with the two sides far apart in talks on Tehran's nuclear program, have pushed up oil prices, and a Russian corvette warship on Thursday joined planned Iranian naval drills in the Gulf of Oman, a vital sea route for global energy.
Iranian and US negotiators met on Tuesday and Iranian Foreign Minister Abbas Araqchi said they had agreed on "guiding principles".
White House press secretary Karoline Leavitt said on Wednesday, however, that the two sides remained apart on some issues.
Trump said "good talks are being had", and a senior US official said Iran would make a written proposal on how to address US concerns.
Trump called on Tehran to join the US on the "path to peace".
"They can't have a nuclear weapon, it's very simple," he said. "You can't have peace in the Middle East if they have a nuclear weapon."
Iran has resisted making major concessions on its nuclear program, though it insists it is for peaceful purposes. The US and Israel in the past have accused Tehran of trying to develop a nuclear bomb.
Earlier on Thursday, Russia warned against an "unprecedented escalation of tension" around Iran on Thursday and urged restraint amid the US military build-up in the region, which a senior American official said should be complete by mid-March.
Trump has sent aircraft carriers, warships and jets to the region, raising the prospect of another attack on the Islamic Republic.
The United States and Israel bombed Iran's nuclear facilities and some military sites last June. US Secretary of State Marco Rubio will meet Israeli Prime Minister Benjamin Netanyahu to discuss Iran on February 28, a senior US official said.
Washington wants Iran to entirely give up uranium enrichment, a process used to create fuel for atomic power plants but that can also provide material for a warhead.
The US and ally Israel also want Iran to give up long-range ballistic missiles, stop supporting groups around the Middle East and stop using force to quell internal protests.
Iran says it refuses to discuss issues beyond the atomic file, calling efforts to limit its missile arsenal a red line.
Iran's joint exercise with Russia came days into an extended series of Iranian naval drills in the Gulf of Oman, with Iranian state television showing special forces units deployed on helicopters and ships.
In a sign of growing concern over the increased tensions, Poland became the latest European country to urge its citizens to leave Iran, with Prime Minister Donald Tusk saying Poles may only have hours to evacuate.
