Kerry met with Ban, Egyptian Foreign Minister Sameh Shoukri and Arab League chief Nabil al-Arabi at a hotel in Cairo, a US official said.
The top US diplomat, who has been locked in meetings in the region since late Monday, has said he plans to speak sometime on Friday.
The United States has worked with Egypt on a plan that, diplomats say, would provide a humanitarian pause in the deadly Israel-Hamas conflict ahead of talks on key issues.
But Israeli public television reported that the Jewish state's cabinet rejected the ceasefire. Hamas, which has been firing rockets into Israel, rejected an earlier Egyptian-drafted ceasefire proposal.
Hamas officials were not immediately available for comment on Friday. The 18-day conflict has killed more than 800 people, most of them Palestinian civilians.