Blinken is set to visit Egypt and Israel on Monday. He also aims to ensure the war does not expand into Lebanon.
"We call upon the U.S. administration to put pressure on the occupation to stop the war on Gaza and the Hamas movement is ready to deal positively with any initiative that secures an end to the war," senior Hamas official Sami Abu Zuhri said.
In his eighth visit to the region since Hamas attacked Israel on Oct. 7, triggering the bloodiest episode in the decades-long Israeli-Palestinian conflict, Blinken is also set to travel to Jordan and Qatar this week.
He is set to meet with Egyptian President Abdel Fattah al-Sisi in Cairo before traveling to Israel later on Monday, where he will meet with Prime Minister Benjamin Netanyahu and Defence Minister Yoav Gallant, according to a State Department schedule.
On Monday, Palestinian residents said tanks had been trying to thrust deeper towards the north in the early hours of Monday, edging Shaboura, one of the most densely populated and Hamas stronghold neighborhoods at the heart of the city.
Israeli tank forces have since seized Gaza's entire border strip with Egypt running through Rafah to the Mediterranean coast and invaded many districts of the city of 280,000 residents, prompting around one million displaced people who had been sheltering in Rafah to flee elsewhere.
Blinken's visit comes after U.S. President Joe Biden on May 31 outlined a three-phase ceasefire proposal from Israel that envisions a permanent end to hostilities, the release of Israeli hostages and Palestinian prisoners, and the reconstruction of Gaza.
The Hamas attack killed 1,200 people and took some 250 others hostage, according to Israeli tallies. In response, Israel launched an assault on the Gaza Strip that has killed more than 37,000 Palestinians, the health ministry in the Hamas-run territory said in its Sunday update.
