LAUSANNE, Switzerland — With 10 days to a nuclear deal deadline, top U.S and Iranian officials spoke Saturday of substantial headway, and Iran’s president proclaimed that agreement was within reach. But America’s top diplomat said it was up to Tehran to make the decisions needed to get there.

Iranian President Hassan Rohani said “achieving a deal is possible” by a March 31 target date for a preliminary accord that is meant to lead to a final deal by the end of June that would crimp Tehran’s nuclear programs in exchange for sanctions relief.

U.S. Secretary of State John Kerry was more circumspect, as he spoke to reporters after six days of negotiations. The talks, made “substantial progress,” he said, but “important gaps remain.”

“We have an opportunity to get this right,” Kerry said, as he urged Iran to make “fundamental decisions” that prove it has no interest in atomic weapons.

But Iran’s supreme leader warned against expectations that even a done deal would mend the more than three-decade freeze between the two nations in place since the Iranian revolution and siege of the American Embassy.

“Negotiations with America are solely on the nuclear issue and nothing else. Everyone has to know that,” Ayatollah Ali Khamenei told a crowd in northeastern Iran on the first day of the Persian new year. “We do not talk with U.S. over regional issues. In the regional issues, America’s goals are completely opposed to our goals.”

Other officials differed on how close the sides were to a deal.

Top Russian negotiator Sergey Ryabkov and Iran’s atomic energy chief Ali Akbar Salehi said in recent days that technical work was nearly done. But French officials insisted the sides were far from any agreement.

For Washington, the stakes are high if the talks miss the March deadline. The White House has warned that a diplomatic failure could lead to an ever tougher dilemma: Whether to launch a military attack on Iran or allow it to reach nuclear weapons capacity.

A more immediate challenge may be intervention from Congress. If American lawmakers pass new sanctions on Iran, the Islamic Republic could respond by busting through the interim limits on its nuclear program it agreed to 16 months ago.

Thus far, it has stuck to that agreement.