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US Secretary of State Antony Blinken met Israel's prime minister Tuesday to push for a ceasefire in Gaza after his administration called for an end to the war on Lebanon "as soon as possible".

It is his 11th trip to the Middle East since 7 October and his first since Israel's conflict with Hezbollah escalated late last month.

His meetings with Israeli Prime Minister Benjamin Netanyahu and other top officials come as Israel weighs its response to Iran's 1 October missile attack.

The Secretary urged Netanyahu on Tuesday to seize on the killing of Hamas's leader to work towards a Gaza ceasefire and pressed for more aid into the Palestinian territory.

Blinken "underscored the need to capitalise on Israel's successful action to bring Yahya Sinwar to justice by securing the release of all hostages and ending the conflict in Gaza in a way that provides lasting security for Israelis and Palestinians alike," State Department spokesman Matthew Miller said after the talks in Jerusalem.

In Lebanon, Israel hit an area of south Beirut housing the country's largest public health facility, killing 13 people, according to the health ministry.

The Rafik Hariri Hospital sustained minor damage in the strike which flattened four nearby buildings, an AFP correspondent reported.

Previous US efforts to end the Gaza war and contain the regional fallout have failed, as did a bid spearheaded by President Joe Biden and his French counterpart Emmanuel Macron to secure a temporary ceasefire in Lebanon.

After Israel, Blinken will visit Jordan on Wednesday and discuss humanitarian aid for the Gaza Strip, an official on the plane with him said.

Blinken also plans to speak to Israeli leaders about the expected strike on Iran and discourage any move that could massively escalate regional conflict, the official said.