But even as the two sides tried to finalize the agreement on Thursday, fissures have widened between the United States and some of its principal allies over the potential pact, which has been hailed by the Obama administration as a possible breakthrough in the standoff over Iran’s nuclear aspirations but dismissed by critics as a temporizing measure that would leave the core of Tehran’s atomic program intact.

Mr. Kerry and senior American officials here have promoted the idea of a multistage agreement as a hardheaded response to the new Iranian leadership of President Hassan Rouhani. The first phase of the accord would suspend Iran’s nuclear effort for as long as six months in return for limited sanctions relief, which could include access to frozen assets.

“We are asking them to step up and provide a complete freeze over where they are today,” Mr. Kerry said Thursday during a trip to the Middle East. “Iran knows that if they don’t meet the standards of the international community, the sanctions could be increased and even worse.”