Brent crude rose 2.8 percent to $107.26 a barrel as of 07:15 GMT, while US West Texas Intermediate gained 1.8 percent to $94.07 per barrel.
Tehran put forward a plan at the UN General Assembly last week calling for a halt in hostilities and the reopening of the strategic waterway.
Iranian officials have said the proposal was intended to ease pressure on global energy supplies by reopening the Strait of Hormuz, a key route for international oil shipments.
Iran has also said that reopening the strait would depend on several conditions, including the release of frozen Iranian assets, the lifting of US sanctions on Iranian oil and an end to the US naval blockade.
Trump, however, told reporters outside the White House, “I reject their proposal.”
At the same time, Trump indicated that negotiations could resume, claiming to Axios that Iran wanted an agreement but that its proposal did not meet his conditions.
Meanwhile, Axios, citing sources familiar with the matter, claimed that indirect talks between Washington and Tehran could take place as early as Monday.
The renewed uncertainty affected global energy markets, with oil prices reversing part of Friday’s decline, when crude had fallen more than 2 percent following reports of the Iranian proposal.
Stephen Innes of Quintex Intel said the rejection had intensified market concerns over the regional situation.
“Middle East tensions have flared again after Trump rejected Iran’s latest proposal to reopen the Strait of Hormuz,” Innes wrote.
“Oil has pushed higher, Asian equities are softer, and suddenly the brief Friday reprieve in global fixed income looks more like an intermission than the end of the show,” he added.
“The market is still pricing some probability that everyone eventually finds their way back to the table, even if they continue to spend the next few weeks shouting across it first.”
The rise in oil prices also returned inflation and interest-rate expectations to the center of investors’ attention.
Bond yields climbed, with the average yield on a gauge of global bonds topping 4 percent last week for the first time since 2007, according to Bloomberg.
The developments are placing renewed attention on the US Federal Reserve ahead of its next policy meeting at the end of October.
Investors are expected to watch the release of the US central bank’s preferred inflation gauge this week, along with a key jobs report that could influence monetary-policy decisions.
Asian markets showed mixed reactions as investors assessed the renewed uncertainty.
Seoul fell 2.7 percent after reopening following a long break, while Tokyo, Shanghai, Manila, Mumbai, Bangkok and Jakarta also declined.
Hong Kong, Sydney, Singapore and Wellington recorded gains, while London, Paris and Frankfurt also moved higher.
The latest market movements came as the Strait of Hormuz remained at the center of international attention because of its importance to global energy supplies.
Iran’s proposal could facilitate the reopening of the waterway and ease pressure on energy markets, but the US rejection of the proposal has dimmed the prospect of renewed indirect negotiations and the status of the Strait of Hormuz as key factors for energy markets.