Trump said he was responding to Iran's earlier call for Washington to meet conditions, including recompensing Tehran for the damage caused since the US and Israel launched strikes on its territory more than five months ago.
"I am likewise demanding compensation from Iran, for all of the people that they have killed and gravely wounded with their roadside bombs and many conflicts, for which they are famous," Trump wrote on his Truth Social service.
Oil prices, which had risen earlier on the Iranian comments, extended gains after Trump's post, with Brent crude up 4.25 per cent at 3.20am AEST Tuesday.
Trump's demand had not previously been raised by the US in talks or statements.
The president said it would be part of all future negotiations with the Iranian leadership and would include calls for payments to the families of hundreds of thousands of protesters whom he said Iran had killed.
Rights groups say the Iranian government has continued to crack down on opponents during the war.
Trump also said Iran should compensate "families of those killed on the USS Cole", a reference to the October 12, 2000, attack on that naval vessel in Yemen which killed 17 US sailors, and has been blamed on al Qaeda, not Iran.
"Also, with respect to the Iran negotiations, Iran should be responsible for the damages and death caused to the people of Lebanon, Syria, Yemen, and Gaza!" Trump wrote in a second post.
Iran had earlier said it was nearing a final pact with Oman defining new shipping lanes between them through the Strait of Hormuz but repeated that the US must meet conditions, including compensation and an end to sanctions and military threats before the key waterway is reopened.
The strait, through which about a fifth of global oil and liquefied natural gas flowed before the conflict, has been effectively blocked since the US-Israeli attacks on Iran on February 28, pushing up oil prices and inflation.
Trump, who has said the attacks on Iran were aimed at keeping the Islamic Republic from developing nuclear weapons and degrading its ability to threaten the region, is under pressure to end a war that is deeply unpopular at home ahead of midterm elections in November.
The tit-for-tat US and Iranian calls for compensation were the latest jolt in a rhetorical rollercoaster that has regularly seen Trump threaten imminent attacks on Iran or hail breakthroughs in talks, only for neither to emerge.
Earlier on Monday, Iranian Foreign Ministry spokesman Esmaeil Baghaei said talks with Oman on arrangements for navigation through the strait were "progressing smoothly and constructively," with an agreement reached on a shipping route map, while some technical issues on a joint statement remained unresolved.
He said during a weekly press conference in Tehran that the discussions also covered mechanisms for safe navigation, environmental protection, maritime services and combating crime, adding that such services would normally entail receiving payment in return.
US officials have repeatedly said they would not accept any deal under which Tehran controlled or charged fees for access to the strait.
But months of US military efforts, including a two-week campaign of strikes in July, have not broken Iran's grip on the strait.
Washington and Tehran agreed to a ceasefire in June, but the US reimposed a blockade on Iranian shipping in the Gulf in July, a move that Tehran said violated the truce, which by then had already broken down.
Iran has been striking back with missiles and drones against Washington's allies in the region, while also targeting commercial ships transiting the strait without its permission.
