Hopes that the two sides could make progress during negotiations in Pakistan were dashed Saturday by the US president, who said there was no point "sitting around talking about nothing".
He said on Fox News that he told his team: "We have all the cards. They can call us anytime they want, but you're not going to be making any more 18-hour flights to sit around talking about nothing."
However, he told reporters a revised proposal from Iran had followed within minutes of his decision.
"They gave us a paper that should have been better and -- interestingly -- immediately, when I cancelled it, within 10 minutes, we got a new paper that was much better," he said, without elaborating.
Asked separately whether the cancellation meant a return to hostilities, Trump said: "No, it doesn't mean that. We haven't thought about it yet."
But even before Trump's move, prospects for talks were uncertain, with Iranian state television saying Foreign Minister Abbas Araghchi had no plans to meet US officials and that Islamabad would act as a conduit for proposals.
Axios on Sunday cited unnamed sources including a US official as saying Tehran had provided a new offer to reopen the Strait of Hormuz -- through which a fifth of global oil and gas passes -- with nuclear talks pushed back to a later date.
Talks between the rivals have reached an impasse, with Iran hitting out at a US blockade of its ports and the White House demanding the Islamic republic allow ships to transit the crucial waterway.
Iranian state media said Monday that Araghchi had arrived in Saint Petersburg for talks with Russian President Vladimir Putin. The trip comes after visits to Islamabad and Oman in a flurry of regional diplomacy.
Soon after landing, Araghchi blamed the United States for the failure of the peace talks citing its "excessive demands", adding that "safe passage through the Strait of Hormuz is an important global issue".
Oil prices rose around two percent Monday, though lingering hopes that a deal can eventually be reached have tempered the gains.
However, Fawad Razaqzada of Forex.com, warned they could surge again at any time.
"If tensions were to escalate further, particularly into open conflict, there's a clear risk of a sharper spike," he wrote.
"For now though, as long as shipping through the Strait remains constrained, that premium is unlikely to fade. Until there's a credible breakthrough, the path of least resistance still looks higher, with a move beyond $110 appearing increasingly plausible."
Stocks fluctuated, with Tokyo, Seoul and Taipei sharply up on the back of AI-fuelled tech gains following US giant Intel's healthy revenue forecasts.
There were also gains in Shanghai, Mumbai, Bangkok and Jakarta, while Hong Kong, Sydney, Singapore and Manila fell.
London fell at the open while Paris and Frankfurt rose.
That came after the S&P 500 and Nasdaq ended Friday at fresh record highs.
Investors were also looking ahead to earnings this week from US tech titans Alphabet, Meta, Microsoft, Amazon and Apple, while the Federal Reserve will hold a closely watched policy meeting at which it is expected to stand pat on interest rates.
- Key figures at 0715 GMT -
West Texas Intermediate: UP 1.9 percent at $96.18 a barrel
Brent North Sea Crude: UP 2.1 percent at $107.51 a barrel
Tokyo - Nikkei 225: UP 1.4 percent at 60,537.36 (close)
Hong Kong - Hang Seng Index: DOWN 0.3 percent at 25,911.28
Shanghai - Composite: UP 0.2 percent at 4,086.34 (close)
London - FTSE 100: DOWN 0.2 percent at 10,362.72
Euro/dollar: UP at $1.1727 from $1.1717 on Friday
Pound/dollar: UP at $1.3537 from $1.3530
Dollar/yen: DOWN at 159.30 yen from 159.42 yen
Euro/pound: UP at 86.63 pence from 86.60 pence
New York - Dow Jones: DOWN 0.2 percent at 49,230.71 (close)
dan/mtp