"He doesn't love the proposal," the official said, referring to Trump.
Earlier in the day, Trump discussed the proposal with his top national security aides. The US-Iran conflict remains in a stalemate with energy supplies from the region reduced.
Iranian sources earlier on Monday said the proposal would set aside discussion of Iran's nuclear program until the war has ended and disputes over shipping from the Gulf are resolved. Washington has said nuclear issues must be dealt with from the outset.
Work to bridge gaps between the US and Iran has not halted, sources from mediator Pakistan said.
Hopes of reviving peace efforts have receded since the US president this weekend announced he had scrapped a visit by his special envoy Steve Witkoff and son-in-law Jared Kushner to Islamabad, the Pakistani capital, where Iranian Foreign Minister Abbas Araqchi shuttled in and out twice during the weekend.
Araqchi 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 on issues including Iran's nuclear ambitions and access to the crucial Strait of Hormuz, oil prices resumed their upward march on Monday, hitting a two-week high.
Araqchi told reporters in Russia that Trump had requested negotiations because the US has not achieved any of its objectives.
Senior Iranian sources, speaking on condition of anonymity, told Reuters the proposal carried by Araqchi to Islamabad over the weekend 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 United States cannot start it up again.
Then negotiators would resolve the US blockade 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 for what it says are peaceful purposes.
Iran also accused the United States of piracy due to Washington's naval blockade targeting Iranian shipping, after the US military intercepted sanctioned Iranian oil tankers at sea.
"This is the outright legalisation of piracy and armed robbery on the high seas," Iranian Foreign Ministry spokesman Esmaeil Baqaei wrote on X.
He said the US actions marked a "return of the pirates - only now, they operate with government-issued warrants."
Fighting has intensified in Lebanon, where Israeli strikes killed 14 people and wounded 37 in the south on Sunday, according to the health ministry, making it the deadliest day since a US-brokered ceasefire was announced in mid-April.
Israel's military said it also carried out fresh strikes on targets belonging to the Iran-backed Hezbollah in Lebanon on Monday.
Iran says it will not hold talks on the wider conflict unless a ceasefire also holds in Lebanon, which Israel invaded in March in pursuit of the militant group Hezbollah which fired across the border in solidarity for Iran.
Israel and Hezbollah blame each other for violating the truce agreed between Israel and the Lebanese government in the US and extended last week.
with DPA
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