JERUSALEM — Israel and its main militant Gaza adversary weighed an Egyptian cease-fire proposal late Monday, signaling a possible de-escalation of a week-old aerial battle that has left nearly 200 Palestinians dead from Israeli bombs and has sent hundreds of Gaza rockets deep into Israeli territory.

A senior government official in Israel, which has been preparing for the possibility of a ground invasion of Gaza, said it was seriously considering the Egyptian proposal. The initial reaction of Hamas, the dominant militant group in Gaza, was less committal, but was not an outright rejection.

The proposal envisioned a cease-fire beginning at 9 a.m. local time on Tuesday. It called for border crossings to Gaza to “be opened,” with the movement of people and goods to be “facilitated once the security situation becomes stable on the ground.” Within 48 hours of the initial cease-fire taking hold, talks are to be held in Cairo with the Israelis and the Palestinian militant factions on conditions for a longer-term truce, according to the text of the proposal.

An Egyptian Foreign Ministry spokesman, Ambassador Badr Abdelatty, said: “We hope it will be acknowledged. We are in close contact with everyone.”