US President Donald Trump said Wednesday that "great progress" was being made to end the Israel-Hamas war in Gaza as a new ceasefire push began more than 20 months since the start of the conflict.

"I think great progress is being made on Gaza," Trump told reporters ahead of a Nato summit in the Netherlands, adding that his special envoy Steve Witkoff had told him "Gaza is very close." He linked his optimism about imminent "very good news" for the Gaza Strip to a ceasefire agreed on Tuesday between Israel and Iran to end their 12-day war.

Israeli Prime Minister Benjamin Netanyahu has also suggested that Israel's blitz of Iran's nuclear and missile facilities, as well as its security forces linked to overseas militant groups, could help end the Gaza conflict.

Key mediator Qatar announced Tuesday that it would launch a new push for a ceasefire.

A senior Hamas official told AFP Wednesday that talks for a Gaza ceasefire with Israel "intensified in recent hours" with mediator countries.

"Our communications with the brother mediators in Egypt and Qatar have not stopped and have intensified in recent hours," Taher al-Nunu said, adding that the group had "not yet received any new proposals" to bring an end to the war now in its 21st month.

The Israeli government declined to comment on any new ceasefire talks beyond saying that efforts to return Israeli hostages in Gaza were ongoing "on the battlefield and via negotiations".

Israel's military campaign has killed at least 56,156 people, also mostly civilians, according to the health ministry in Gaza.

Gaza's civil defence agency said Wednesday that Israeli fire killed at least another 20 people, including six who were waiting for aid.

The Gaza health ministry says that since late May, nearly 550 people have been killed near aid centres while seeking scarce supplies.