TEL AVIV (Reuters) - U.S. Secretary of State Antony Blinken on Wednesday kicked off a series of meetings with Israeli leaders discussing how to get more humanitarian aid into Gaza while at the same time repeatedly urged Palestinian militant Hamas to accept a deal offer that will release hostages and achieve a ceasefire.

Following visits to Riyadh and Amman earlier this week, the top U.S. diplomat is now in Israel for the final stop of his wider Middle East tour.

It is Blinken's seventh visit to the region which was plunged into conflict on Oct. 7 when Hamas attacked Israel.

Blinken's top priority in Israel will be to push the Israeli government to take a set of specific steps so that improvements in the humanitarian aid flow into the densely populated enclave.

"Even as we're working with relentless determination to get the ceasefire that brings the hostages home, we also have to be focused on people in Gaza for suffering in this crossfire of Hamas' making," Blinken said in remarks at the start of his meeting with Israeli President Isaac Herzog in Tel Aviv.

"Focused on getting them the assistance they need, the food, and medicine, the water or shelter is also very much on our minds," Blinken said.

Hamas killed 1,200 people and abducting 250 others in its Oct. 7 assault on Israel, according to Israeli tallies.

In response, Israel has launched a relentless assault on Gaza, killing more than 34,000 Palestinians, local health authorities say, in a bombardment that has reduced the enclave to a wasteland. More than one million people face famine after six months of war, the United Nations has said.

Blinken's check-in with Netanyahu on aid will take place about a month after U.S. President Joe Biden issued a stark warning to Netanyahu, saying Washington's policy could shift if Israel fails to take steps to address civilian harm, humanitarian suffering, and the safety of aid workers.

Biden has threatened to condition support for Israel's offensive in Gaza on it taking concrete steps to protect aid workers and civilians, seeking for the first time to leverage U.S. aid to influence Israeli military behavior.

U.N. Secretary-General Antonio Guterres said on Tuesday there had been incremental progress toward averting "an entirely preventable, human-made famine" in the northern Gaza Strip, but called on Israel to do more.

The first shipments of aid directly from Jordan to northern Gaza's newly opened Erez crossing will leave on Tuesday, goods are also arriving via the port of Ashdod, and a new maritime corridor will be ready in about a week, Blinken said.

(Reporting by Humeyra Pamuk; Editing by Michael Perry)

By Humeyra Pamuk