Six weeks since Trump paused Operation Epic Fury for a ceasefire, talks to end the war have shown little progress.
Trump said this week he came close to ordering more attacks but held off to allow time for negotiations.
"We're in the final stages of Iran. We'll see what happens. Either have a deal or we're going to do some things that are a little bit nasty, but hopefully that won't happen," he told reporters.
"Ideally I'd like to see fewer people killed as opposed to a lot. We can do it either way."
Speaking later at the US Coast Guard Academy, Trump reprised his either/or rhetoric - "We may have to hit them very hard ... but maybe not" - and reiterated his determination not to allow Iran to acquire a nuclear weapon.
Iran, for its part, accused Trump of plotting to restart the war, and threatened to retaliate for any strikes with attacks beyond the Middle East.
"If aggression against Iran is repeated, the promised regional war will extend beyond the region this time," the Revolutionary Guards said in a statement.
Parliament Speaker Mohammad Baqer Qalibaf, Iran's top peace negotiator, said in an audio message on social media that "obvious and hidden moves by the enemy" showed the United States was preparing new attacks.
Foreign ministry spokesman Esmaeil Baghaei later said the US had to end its "piracy" against Iranian ships - a reference to the US blockade of Iranian ports.
"Despite the negative record of the other side over the past year and a half, Iran is pursuing the path of negotiations with seriousness and good faith but it has strong and reasonable suspicion over America's performance," Baghaei said.
In the latest diplomatic push, the interior minister of Pakistan - which hosted the only round of peace talks so far and has since been the conduit for messages between the sides - was in Tehran on Wednesday.
Baghaei said the US and Iran continued to exchange messages through the Pakistani minister's mediation.
Iran submitted a new offer to the United States this week.
Iran's descriptions suggest it largely repeats terms previously rejected by Trump, including demands for control of the Strait of Hormuz, compensation for war damage, lifting of sanctions, release of frozen assets and the withdrawal of US troops from the area.
Trump has said he called off attacks this week at the last minute in response to requests from several of Iran's Gulf neighbours.
Iran has largely shut the Strait of Hormuz to all ships apart from its own since the US-Israeli campaign began in February, causing the biggest disruption to global energy supplies in history.
The US responded last month with its own blockade of Iran's ports.
Iran says it aims to reopen the strait to friendly countries that abide by its terms.
That could potentially include fees for access, which the US says would be unacceptable.
Baghaei said late on Wednesday that Iran was ready to establish with Oman a mechanism to ensure sustainable security in the Strait of Hormuz.
Two giant Chinese tankers laden with a total of about four million barrels of oil exited the strait on Wednesday.
Iran had announced last week, while Trump was in Beijing for a summit, that it had agreed to ease rules for Chinese ships.
South Korea's foreign minister said on Wednesday a Korean tanker was crossing the strait in cooperation with Iran.
Shipping monitor Lloyd's List said at least 54 ships had transited the strait last week, about double the previous week.
Iran said 26 ships had crossed in the past 24 hours, still only a fraction of the 140 per day before the war.
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