CAIRO — Secretary of State John F. Kerry broadened the U.S. effort to reach a cease-fire in Gaza on Tuesday, seeking to revive a truce proposal rejected by Hamas militants a week ago. Kerry met early Tuesday with the intelligence chief of the Palestinian Authority, Majid Faraj, and later with Egyptian Foreign Minister Sameh Shoukry, who suggested that a cease-fire be linked to a larger effort to resume failed Israeli-Palestinian peace talks.