CAIRO/JERUSALEM (Reuters) - Israeli shelling and airstrikes killed at least 19 people in central and south Gaza on Tuesday including two policemen who were helping protect humanitarian aid deliveries in the southern city of Rafah, Palestinian medics said.

Seventeen of the deaths, they said, occurred in separate Israeli airstrikes on the al-Bureij and al-Maghazi refugee camps and the city of Deir-al-Balah in central Gaza, and by late Tuesday tanks were shelling an area just east of the al-Nusseirat camp, residents said.

Some told Reuters via chat app that the renewed Israeli military push was sowing panic, with some families living in al-Maghazi starting to flee under tank fire, with four shells crashing near a clinic in the camp.

In a brief statement issued earlier in the day, the Israeli military said jets were hitting Hamas militant targets in central Gaza while ground forces were operating "in a focused manner with guidance from intelligence" in the al-Bureij area.

It gave no update on activity in Rafah, into which Israeli forces swept last month in what the military calls a limited operation to root out Hamas' last intact combat units after almost eight months of devastating war in the Gaza Strip.

The small city fringing Gaza's southern border with Egypt had been sheltering about one million Palestinians who fled Israeli assaults in other parts of the enclave, but most have fled again in the face of Israel's tank-led advance.

Israel launched an air and ground offensive in Gaza last October vowing to destroy Hamas after militants stormed across the border into southern Israel on Oct. 7, killing around 1,200 people and taking more than 250 people hostage, according to Israeli tallies. About 120 hostages remain in Gaza.

The Israeli military campaign has killed more than 36,000 people in densely populated Gaza, according to its health authorities, who say thousands more bodies are buried under rubble.

Qatar said on Tuesday it had delivered an Israeli ceasefire proposal to Hamas that reflected a three-phase proposal presented on Friday by U.S. President Joe Biden, and that the paper was now much closer to the positions of both sides.

Qatar, which has been mediating on Gaza between Israel and Hamas, also stressed that there should be a clear position from both parties to clinch a deal, its foreign ministry spokesperson said in a press briefing.

"The ceasefire deal should immediately end the long suffering of all people in Gaza and the hostages and their families and provide a roadmap for a permanent ceasefire and an end to the (humanitarian) crisis", Majed al-Ansari said.

However, a spokesman for Hamas, the Islamist militant group that has ruled Gaza since 2007, reiterated on Tuesday it could not agree to any deal unless Israel makes a "clear" commitment to a permanent truce and complete withdrawal from Gaza.

For his part, Israeli Prime Minister Netanyahu repeated that there can be no permanent peace unless Hamas is eradicated, as he struggles with profound political divisions at home over the U.S.-backed truce proposal.

An aide to Netanyahu said on Sunday Israel had accepted the framework advanced by Biden, though he described it as flawed and in need of much more work.

On Tuesday, his biggest coalition partner said it would support such a deal even if it entails an overhaul of the war strategy. But Netanyahu's far-right allies in the government threatened to bolt and bring it down if he wound down the Gaza war without having annihilated Hamas.

Biden's framework proposal involves in its first stage a six-week ceasefire when Israeli forces would withdraw from "all populated areas" of Gaza and some hostages - including the elderly and women - would be freed by Hamas in exchange for hundreds of Palestinian prisoners.

Under that plan, Hamas and Israel would negotiate in the same phase a permanent ceasefire that Biden said would last "as long as Hamas lives up to its commitments."

In the second phase, Biden said there would be an exchange for all remaining living hostages, including male soldiers, Israeli forces would withdraw from Gaza and the permanent ceasefire would begin. The last stage of the plan would include the reconstruction of the shattered coastal enclave.

Biden's Middle East envoy, Brett McGurk, will travel to the region this week to push for a hostage deal and ceasefire, a U.S. official told Reuters on Tuesday.

(Reporting by Henriette Chacar in Jerusalem and Nidal al-Mughrabi in Cairo; Writing by Mark Heinrich; editing by William Maclean)

By Nidal al-Mughrabi and Henriette Chacar