GENEVA — After years of fruitless negotiations, Western and Iranian diplomats are on the verge of an agreement that would freeze Tehran’s nuclear program in exchange for an easing of some economic sanctions.

Secretary of State John Kerry is scheduled to travel here on Friday at the invitation of Catherine Ashton, the European Union’s foreign policy chief, in an effort “to help narrow differences,” a senior State Department official said. If that goes well, the pact could be announced later in the day, Iranian officials said.

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.