International powers negotiating a nuclear deal with Iran failed to meet another deadline on Tuesday, the second missed target in a week, raising the prospect of an open-ended diplomatic process over an issue on which President Barack Obama has staked his foreign-policy record.

Senior administration officials in Vienna and Washington said progress was still being made and negotiators “have never been closer” to a comprehensive deal to curb Iran’s nuclear program in exchange for lifting international sanctions. Mr. Obama has said talks would end in a deal that reflects a framework reached in April, or with no agreement at all.

But with negotiations making little headway, the White House on Tuesday laid the groundwork for a third outcome: continuing talks while keeping in place a November 2013 interim agreement that provided Iran with limited sanctions relief in exchange for rolling back parts of its nuclear program.

Such an outcome would allow Mr. Obama to avoid alternatives to diplomacy to confront Iran’s nuclear program, such as military force.