The Palestinian resistance group Hamas said Sunday it was ready to "immediately" hold a fresh round of negotiations for a truce in Gaza after recent talks appeared to hit a dead end.

"The movement affirms its readiness to immediately begin a round of indirect negotiations to reach an agreement on the points of contention," Hamas said in a statement after mediators Qatar and Egypt said they would intensify their efforts for a truce in the war-battered Gaza Strip.

According to Gaza's civil defence agency, Israeli gunfire killed at least 31 Palestinians near a US-backed aid distribution site Sunday, with both the group in charge of the site and the military denying any such incident took place.

Israel has faced growing condemnation over the humanitarian crisis in the war-ravaged Gaza Strip, where the United Nations has warned the entire population faces the risk of famine after no aid was allowed to enter for more than two months.

Israel recently eased its blockade and introduced a revamped aid mechanism in cooperation with a newly formed US-backed organisation, the Gaza Humanitarian Foundation (GHF), bypassing the longstanding UN-led system.

Civil defence spokesman Mahmud Bassal said that "31 people were killed and more than 176 injured... after Israeli gunfire targeted thousands of civilians near the American aid centre in Rafah", in southern Gaza.

Near another GHF aid centre in central Gaza, images showed rescuers evacuating injured people. Bassal reported one dead and dozens wounded there, again blaming Israeli fire.

A GHF spokesperson denied any deaths or injuries took place.

Speaking about the reported deaths to US broadcaster ABC, World Food Programme Executive Director Cindy McCain said "our people are reporting the same thing on the ground".

"It's a tragedy. And what we need right now is an immediate ceasefire, complete, unfettered access... to feed people and stop this catastrophe from happening," she added.

Only limited amounts of aid have entered Gaza since Israel eased its total blockade that began in March.

Nearly 20 months into the war, negotiations for a ceasefire and hostage release deal have failed to produce a breakthrough.

Since the last brief truce collapsed in March, Israel has intensified its operations.

Israeli Defence Minister Israel Katz, meanwhile, said he had told the army "to continue forward in Gaza against all targets, regardless of any negotiations".

The health ministry in Hamas-run Gaza says at least 4,149 people have been killed in the territory since Israel resumed its offensive on March 18, taking the war's overall toll to 54,418, mostly civilians.