"We very much want to bring this over the finish line in the next two weeks, the time we have remaining," Blinken told a news conference in South Korea when asked whether a ceasefire deal was close.
Israel has sent a team of mid-ranking officials to Qatar for talks brokered by Qatari and Egyptian mediators.
Some Arabic media reports said David Barnea, the head of Mossad who has been leading negotiations, was expected to join them.
The Israeli prime minister's office did not comment.
It remains unclear how close the two sides remain, with some signs of movement but little indication of a shift in some of the key demands that have so far blocked any truce for more than a year.
US president-elect Donald Trump has said there would be "hell to pay" in the Middle East if hostages held by Hamas were not freed before his inauguration on January 20, now viewed in the region as an unofficial deadline for a truce deal.
US Secretary of State Antony Blinken wants a Gaza deal before US President Joe Biden's term ends. (AP PHOTO)
According to Gaza Strip health officials, nearly 46,000 Palestinians have been killed in Israel's assault on the enclave.
The assault was launched after Hamas fighters stormed Israeli territory in October 2023, killing 1200 people and capturing more than 250 hostages, by Israeli tallies.
More than 100 hostages are still believed to be held in the Gaza Strip and Hamas says it will not free them without an agreement that ends the war with Israeli withdrawal.
Israel says it will not halt its assault until Hamas is dismantled as a military and governing power and all hostages go free.
A Hamas official told Reuters the group had cleared a list submitted by Israel of 34 hostages who could be freed in the initial phase of a truce.
The list provided by the official included female soldiers plus elderly, female and minor-aged civilians.
Israeli Prime Minister Benjamin Netanyahu's office said the list had been given by Israel to Qatari mediators as far back as July, and Israel had so far received no confirmation or comment from Hamas about whether the hostages on it were alive.
For Michael Levy, whose brother Or was one of the 34 names on the list, there was little comfort.
"The way I see this list is the way I saw all the recent rumours about an upcoming deal," he told Reuters.
"For me, as long as my brother is not here and the hostages are not here in Israel, it's just a rumour."
Israeli forces, which have intensified their operations in recent weeks, continued bombardments across the enclave, killing at least 48 people and wounding 75 over the past 24 hours, according to the Gaza health ministry.
Harsh winter weather continued to exact a toll on the hundreds of thousands displaced into makeshift shelters, with officials saying a 35-day-old baby had died of exposure, at least the eighth victim of the cold in the past two weeks.
Officials from al-Awda Hospital in Nuseirat in the central Gaza Strip said an Israeli air strike at a school compound sheltering displaced families had wounded at least 40 people.
While Israel's military says Hamas has largely been destroyed as an organised military force, its fighters continue to hold out in the rubble of Gaza, which has been largely reduced to wasteland by the months of bombardment.
On Monday, two Israeli soldiers were severely wounded in northern Gaza, and three rockets were fired from Gaza, one of which hit a building in the nearby Israeli city of Sderot without casing casualties, Israeli police said.
Separately, the World Food Programme said Israeli forces had opened fire on one of its convoys as the vehicles moved from the centre of the Gaza Strip to Gaza City in the north.
There was no immediate comment from the Israeli military.
In the Israeli-occupied West Bank, a separate Palestinian territory where violence has also surged since the start of the Gaza war, gunmen killed three Israelis and wounded several others when they opened fire on a car and bus near the Israeli settlement of Kedumim.
