The delay is another hurdle in the Trump administration’s push to secure an agreement that would curb Iran’s nuclear program.
President Trump attributed his decision to divisions among the Iranians about how to proceed and said he wanted to give them more time.
Publicly, Iranian officials refuse to confirm a second round of negotiations with the United States, even as they privately say they are making plans to attend.
With the two-week cease-fire almost over, Vice President JD Vance was expected to head to Pakistan on Tuesday for the second round of negotiations.
The vice president is again center stage, after abruptly leaving the first round of high-level Iranian peace talks without an agreement.
President Trump had said that Israeli and Lebanese leaders would speak directly, but a Lebanese official said the country’s president had rejected the idea.
The president did not say who would represent the United States in a potential next round of direct talks, though he ruled out being personally involved.
The United States proposed a 20-year “suspension” of all nuclear activity, even as President Trump demands assurances that Iran can never build a nuclear weapon.
Vice President JD Vance led the highest-level talks between the United States and Iran in nearly 50 years.
Iran sees American demands as reaching far beyond what the United States achieved in war. Tehran is gambling that it can withstand further bombardment more than Washington is willing to sustain economic chaos, experts say.