Ahead of the move, the Israeli military has said there are still 212 people being held hostage in Gaza.
US secretary of state Antony Blinken said on Sunday he is hopeful more will soon be released, but warned he sees “potential” for the conflict to escalate across the Middle East.
Beyond Gaza and the West Bank, Israeli troops have been locked in clashes on the northern border with Lebanon, where Iranian-backed Hezbollah militants have been increasing their attacks.
Prime Minister Benjamin Netanyahu has warned the group not to enter the war, vowing a response that would be “devastating” for Lebanon.
There are also concerns about the possible role of Iran, an ally of Hezbollah.
Meanwhile, the UN has said lorries carrying aid must continue to be allowed into Gaza.
A second convoy of 19 trucks reportedly entered on Sunday after 20 were allowed through the Rafah crossing from Egypt yesterday, but the UN has said at least 100 a day are needed to cover urgent food and medical needs.