The Israel Defense Forces said Tuesday that it took control of the Gazan side of the Rafah crossing with Egypt overnight, marking its first ground incursion into the southern Gazan city. Wael Abu Omar, a Gaza border official, said travel and the flow of aid into the Strip “stopped completely” as a result. Hamas said it agreed to a Qatari-Egyptian cease-fire and hostage-release proposal, and Israel said it would send mediators to Egypt on Tuesday to negotiate a deal, renewing hopes for a pause in fighting even as it vowed to press on with its military operation in Rafah.