Nearly a month into the war, the United States and Iran struggled to find a way to begin negotiations over peace terms on Wednesday, with each insisting it had the upper hand in the conflict and that the other was desperate for a way out.

The United States circulated a 15-point peace plan, diplomats said, demanding what would amount to a complete termination of Iran’s nuclear program and sharp limits on the reach and size of their missile arsenal. It bore strong resemblance to the U.S. demands in February, during negotiations that collapsed when the United States and Israel struck Iran on Feb. 28.

But the Iranian government, in a statement issued through state television, declared it would not end the conflict unless the United States paid war reparations and recognized “Iran’s exercise of sovereignty over the Strait of Hormuz,” suggesting it would continue to decide which ships pass through the narrow strait and which remained bottled up, unable to deliver oil or fertilizer.

The messages between the two countries were being passed by Pakistan, which was trying to assemble peace talks in the capital of Islamabad, proposing dates as soon as this weekend. But neither Iran nor the United States would confirm such discussions, each wanting to avoid seeming the overeager party in a conflict where each wants to demonstrate it holds the upper hand.

The White House press secretary, Karoline Leavitt, ran through a series of military metrics to make the case that Iran’s forces have been crushed — its navy sunk, its missiles destroyed before they could be launched — and said “that’s why you are beginning to see the regime look for an exit ramp.” But she later warned that Iran’s surviving leaders would bring more destruction to the country “if they fail to understand that they have been defeated militarily.”