Iran's latest proposal would set aside discussion of Iran's nuclear program until the war, on hold following a ceasefire announced earlier in April, is ended and disputes over shipping from the Gulf are resolved.
Trump was unhappy with Iran's proposal as he wanted nuclear issues dealt with from the outset, said a US official briefed on the president's Monday meeting with his advisers, speaking on condition of anonymity.
White House spokeswoman Olivia Wales said the US had "been clear about our red lines", as it seeks to end the war it began in February alongside Israel.
A previous agreement in 2015 between Iran and other countries including the US sharply curtailed Iran's nuclear program, which it has long maintained is for peaceful, civilian purposes.
But that deal fell apart when Trump unilaterally withdrew from it in his first term in office.
Hopes of reviving peace efforts have receded since the US president scrapped a visit planned for April 25-26 by his special envoy Steve Witkoff and son-in-law Jared Kushner to mediator Pakistan.
Iranian Foreign Minister Abbas Araqchi shuttled in and out of Islamabad twice at the weekend.
He also visited Oman and on Monday went to Russia, where he met President Vladimir Putin and received words of support from a longstanding ally.
With the warring sides still seemingly far apart, oil prices resumed their upward march, rising nearly three per cent on Tuesday.
At least six tankers loaded with Iranian oil have been forced back to Iran by the US blockade in recent days, underscoring the war's impact on traffic.
Iran's foreign ministry condemned US action against Iran-linked tankers as "outright legalisation of piracy and armed robbery on the high seas".
However, government spokeswoman Fatemeh Mohajerani told state media on Tuesday that Iran had prepared for maritime blockade scenarios as early as the US 2024 presidential election and made necessary arrangements so that "there is nothing to worry about".
She said Tehran was using northern, eastern and western trade corridors that did not rely on Gulf ports to neutralise the blockade's effects.
Between 125 and 140 ships usually crossed in and out of the strait daily before the war, but only seven have done so in the past day, according to Kpler ship-tracking data and satellite analysis from SynMax, and none of them were carrying oil bound for the global market.
With his approval ratings falling, Trump faces domestic pressure to end a war for which he has given the US public shifting rationales.
Senior Iranian officials, speaking on condition of anonymity, told Reuters the proposal carried by Araqchi to Islamabad envisioned talks in stages, with the nuclear issue to be set aside at the start.
A first step would require ending the US-Israeli war on Iran and providing guarantees that the US cannot start it up again.
Then negotiators would resolve the US Navy's blockade of Iran's trade by sea and the fate of the Strait of Hormuz, which Iran aims to reopen under its control.
Only then would talks look at other issues, including the longstanding dispute over Iran's nuclear program, with Iran still seeking some kind of US acknowledgement of its right to enrich uranium.
