GENEVA — With only a month to go before a deadline for a nuclear accord with Iran, Secretary of State John Kerry began a major push Saturday to conclude the agreement.

Mr. Kerry and Mohammad Javad Zarif, the Iranian foreign minister, met here Saturday for six hours of talks, the first high-level negotiating round since the two sides settled on the outline of an agreement on April 2 in Lausanne, Switzerland.

A senior American official, who spoke on the condition of anonymity about the closed meeting, said afterward that the discussions had been “intense at times, but very focused and very comprehensive.” The Obama administration still believes it is possible to complete an accord by the June 30 deadline, and it is determined to try hard to get it done, officials said.

But some experts outside the government have begun to question the wisdom of negotiating against a deadline, especially because some major issues remain unresolved. Rushing an accord, they say, might work to Iran’s advantage by building pressure on the United States and its negotiating partners to make concessions in talks with Iranian officials who have a penchant for hammering out compromises at the last minute.