The combined death toll from attacks on Israel by the Palestinian Islamist group Hamas and retaliatory strikes by the Israeli military has climbed above 1,000.

Israeli media outlets report that Hamas attacks have left at least 600 people dead and more than 2,000 others wounded in Israel. The attacks include Saturday's rocket barrages and militant assaults in Israeli communities.

Reuters news agency reports it was "the deadliest day for Israel since the 1973 war."

Hamas, which controls the Gaza Strip, said on Sunday that it has succeeded in sending more fighters into Israel and that they are destroying enemy targets.

The Israeli military said its troops have neutralized hundreds of Hamas terrorists. But it admitted that fighting was still underway in southern Israel and elsewhere.

The Israeli military is also continuing airstrikes in Gaza, saying its troops are attacking Hamas terrorist facilities.

Health authorities in Gaza said on Sunday that Israeli military strikes have killed 413 people.

Israel says many of its soldiers and civilians have been abducted and held hostage. It says it is evacuating residents from communities near Gaza and has deployed tens of thousands of troops in areas close to the territory.

Analysts are closely watching whether Israel will launch a ground invasion.

More than 2,200 people, including civilians, died on the Palestinian side when Israeli ground troops invaded Gaza in 2014.