CAIRO (Reuters) - Israeli forces killed at least 18 Palestinians on the second day of a stepped-up military offensive in the Gaza Strip on Tuesday that Islamist militant group Hamas said was jeopardizing ceasefire talks.

Qatari and Egyptian mediators, backed by the United States, have accelerated their efforts this week to seal a ceasefire deal aimed at ending the Gaza war and releasing Israeli hostages in Gaza in return for Palestinians prisoners jailed in Israel.

On Tuesday, Israeli tanks deepened their incursion into some Gaza City districts such as Shejaia, Sabra and Tel Al-Hawa, where residents reported the previous day some of the most fierce fighting since the start of the war.

Following Israeli evacuation orders, thousands of people were forced to leave their homes in Gaza City in the north of the territory and head westward towards the Mediterranean coast and to the south.

The assault "could bring the negotiation process back to square one," Hamas quoted leader Ismail Haniyeh as saying on Monday.

The armed wings of Hamas and the Islamic Jihad said they fought against Israeli forces in Tel Al-Hawa with anti-tank rockets and mortar fire, and inflicted casualties. There was no immediate response from the Israeli military on those claims.

In a statement, the Israeli military said troops were continuing operations in Gaza City, following intelligence indicating the presence of Hamas and Islamic Jihad in the area. It said Israeli forces had taken out of action dozens of fighters and located numerous weapons.

Palestinian health officials said an Israeli airstrike killed six people in a house in Gaza City, while nine others were killed in another strike on two houses in Al-Nuseirat and Deir Al-Balah in central Gaza. An Israeli airstrike in Tel Al-Sultan in western Rafah on the Gaza Strip's southern edge killed three Palestinians, medics said.

The war was triggered Oct. 7 when fighters led by Hamas, which controlled Gaza, attacked southern Israel, killing 1,200 people and taking around 250 hostages, according to Israeli figures.

More than 38,000 Palestinians have been killed in the Israeli military offensive since then, according to Gaza health officials.

(Reporting and writing by Nidal al-Mughrabi; Editing by Ros Russell)

By Nidal al-Mughrabi