GAZA CITY — Israel signaled Monday it was winding down its four-week-old war against Palestinian militants in the Gaza Strip, pulling ground forces back to the border fence, declaring it had rooted out all the infiltration tunnels its troops it had found, and agreeing to a three-day truce beginning Tuesday morning, this one urged by Egyptian mediators.

Monday saw a noticeable fall-off in hostilities during a truce declared by Israel alone. But it remained uncertain whether the government of Prime Minister Benjamin Netanyahu would agree in coming days to a negotiated end to the conflict.

Another possibility was that it would taper off the fighting unilaterally, while continuing to utilize targeted airstrikes like the one early Monday that killed a commander of Islamic Jihad, an ally of Hamas, the militant groups that runs Gaza and was Israel’s main antagonist.

Talks were to take place in coming days in Cairo, where a Palestinian delegation has been meeting with Egyptian officials and an Israeli delegation was expected to travel soon, said a senior official involved in the mediation effort.

Azzam Ahmad, head of the Palestinian delegation, said indirect negotiations would begin during the cease-fire, and the Egyptian Foreign Ministry said it was ready to receive the various parties.

Over the past two weeks, previous high-profile cease-fire bids have failed.

But with international condemnation swelling as the Palestinian death toll in four weeks of fighting neared 1,900 – plus the deaths of more than 60 of its own troops – Israel’s motives for continuing an all-out assault in Gaza appeared to be fading.

At the same time, a pair of relatively small-scale attacks in Jerusalem – one carried out with a piece of construction equipment – rekindled fears repercussions could spread to the West Bank and Palestinian neighborhoods of east Jerusalem if the fighting went on.

Monday’s pause in hostilities, which began at 10 a.m. local time, did not apply to Rafah, at the strip’s southern tip, which has been the scene of heavy fighting since Friday morning.

Those clashes precipitated the breakdown of the last brief cease-fire, one of several to collapse soon after being declared.