CAIRO — Israel and the Hamas militant group accepted an Egyptian cease-fire proposal Sunday, clearing the way for the resumption of talks on a long-term truce to end a month of heavy fighting in the Gaza Strip that has taken nearly 2,000 lives.

The announcement marked the second time in less than a week that the bitter enemies had agreed to Egyptian mediation. A similar three-day truce last week collapsed in renewed violence over the weekend.

The truce took effect at midnight (2101 GMT), preceded by heavy rocket fire toward Israel. In Cairo, the Egyptian Foreign Ministry said the cease-fire would allow humanitarian aid into battered Gaza neighborhoods and the reopening of indirect talks on a more lasting and comprehensive deal.

Hamas is seeking an end to the Israeli-Egyptian blockade against Gaza, while Israel wants Hamas to dismantle its formidable arsenal of rockets and other weapons.

Palestinian negotiators accepted the proposal early Sunday after meeting with Egyptian officials throughout the weekend. Israeli officials concurred later. Both delegations are back in Cairo.

Qais Abdelkarim, a member of the Palestinian delegation, said indirect talks with the Israelis would begin Monday “with the hope of reaching a lasting cease-fire.” The goal, he added, was to end the blockade, which he called “the reason for the war.”

The recent fighting has been the heaviest between Israel and Hamas since Hamas took control of Gaza in 2007. More than 1,900 Palestinians have been killed, including hundreds of civilians. On the Israeli side, 67 people have been killed, including three civilians. Nearly 10,000 people have been wounded and thousands of homes destroyed.

The fighting ended in a three-day cease-fire last Tuesday. Egypt had hoped to use that truce to mediate a long-term deal. But when it expired, militants resumed their rocket fire, sparking Israeli reprisals. The violence continued throughout the weekend, including a burst of fighting late Sunday ahead of the expected cease-fire.

The Israeli military reported some 30 rocket attacks from Gaza on Sunday. Palestinian medical officials said seven people were killed in Israeli airstrikes, including the bodyguard of a Hamas leader, the medical officials said.

Israel had walked away from cease-fire talks over the weekend. “Israel will not negotiate under fire,” Prime Minister Benjamin Netanyahu said earlier Sunday, warning that his country’s military campaign “will take time.”

Last week’s talks failed in part because Israel rejected Hamas’ demand for a complete end to the blockade. Israel says the closure is necessary to prevent arms smuggling, and officials do not want to make any concessions that would allow Hamas to declare victory.

A senior Palestinian negotiator acknowledged that the Palestinians would make more modest demands this time around. He said they will seek an end to the bloodshed in Gaza and an easing — but not an end — to the blockade.

“We might not get everything we want, particularly on freedom of movement. But we believe the Israelis and the world have gotten the point that Gazans should live normally and things should be much better than today,” the negotiator said, speaking on condition of anonymity because he was discussing internal Palestinian deliberations.

Israel says Hamas must disarm. Hamas has said handing over its arsenal, which is believed to include several thousand remaining rockets, is out of the question.

The blockade has greatly limited the movement of Palestinians in and out of the impoverished territory of 1.8 million people for jobs and schooling. It has also limited the flow of goods into Gaza and blocked virtually all exports.

An Egyptian crackdown on smuggling tunnels along Gaza’s southern border has made things even tougher by robbing Hamas of its key economic pipeline and weapons conduit. Gaza’s unemployment rate surpasses 50 percent, and Hamas is unable to pay the salaries of tens of thousands of workers.

An easing of the blockade could mean an increased role for Western-backed Palestinian President Mahmoud Abbas, whose forces were ousted by Hamas seven years ago. Officials said the rival Palestinian factions were already exploring options that would give Abbas, who now governs in the West Bank, a foothold in Gaza, including the likely control of its border crossing with Egypt.

At a minimum, Israel will want guarantees that the rocket fire will stop. A 2012 cease-fire promised an easing of the blockade but was never implemented — in part because of sporadic rocket attacks by various armed factions in Gaza.

Israeli Justice Minister Tzipi Livni said Hamas could get the blockade lifted by accepting longstanding international demands to renounce violence and recognize Israel’s right to exist.

“They want to get legitimacy as a terrorist organization without accepting the requirements of the international community,” she told a news conference.

In the West Bank, Palestinian health officials said an 11-year-old boy was shot and killed Sunday by Israeli forces in a refugee camp near the city of Hebron.

Witnesses and relatives of the boy said Israeli security forces opened fire at Palestinian stone-throwers. They said the boy was standing on the road in front of his home at the time.

The military said its forces encountered a “violent riot” and opened fire. It acknowledged that the boy was killed in the violence and said it was investigating.

The current Gaza war escalated from the abduction and killing of three Israeli teens in the West Bank in June. Israel blamed the killings on Hamas and launched a massive arrest campaign, rounding up hundreds of its members in the West Bank. Hamas and other militants unleashed rocket fire from Gaza.