Gaza's Islamist rulers Hamas announced Monday they have reached a Qatari-mediated deal to end more than three weeks of cross-border exchanges of fire with Israel.

After talks with Qatari envoy Mohammed el-Emadi, "an understanding was reached to rein in the latest escalation and end (Israeli) aggression against our people," said the office of the Palestinian territory's Gaza leader Yahya Sinwar.

In the latest escalation, Israel has bombed Gaza almost daily since August 6, in response to airborne incendiary devices and, less frequently, rockets launched across the border.

The fire bombs -- crude devices fitted to balloons, inflated condoms or plastic bags -- have triggered more than 400 blazes and damaged swathes of farmland in southern Israel, according to the fire brigade.

An Egyptian delegation had been shuttling between the two sides to try to broker a renewal of an informal truce under which Israel committed to ease its 13-year-old blockade of Gaza in return for calm on the border.

It was joined by Emadi, who also held talks with Israeli officials in Tel Aviv.

A Hamas source told AFP there had been "a total halt" to balloon and other attacks against Israel, in agreement with other factions in the coastal strip, home to some two million people.

"Fuel supplies will return and the power station will be restarted from Tuesday," the source said.

A punitive Israeli-imposed ban on fuel deliveries cut electricity supplies to just four hours a day, supplied from the Israeli grid.

Financial aid from gas-rich Qatar has been a major component of a truce first agreed in November 2018 and renewed several times since.

Israel had also agreed to take other steps to alleviate unemployment of more than 50 percent in Gaza, but disagreements over implementation have fuelled repeated flare-ups.

These escalated into full-blown conflict in 2008, 2012 and 2014, and mediators have been working to prevent a new war.