Joe Biden has said he is "optimistic" that a Gaza ceasefire deal can be reached.
"We are closer than we’ve ever been," the US president said following the latest round of talks, adding he was sending his secretary of state to Israel to continue the "intensive efforts to conclude this agreement".
Amid concerns that Iran may launch an attack on Israel for the assassination of Hamas leader Ismail Haniyeh in Tehran, Mr Biden said "no-one in the region should take actions to undermine this process".
Hamas has expressed scepticism about the chances of a deal. And without mentioning the possibility of a ceasefire, Israel said it "appreciates the efforts of the US and the mediators to dissuade Hamas from its refusal to a hostage release deal".
The Israeli military launched a campaign in Gaza to destroy Hamas in response to an unprecedented attack on southern Israel on 7 October, during which about 1,200 people were killed and 251 taken hostage.
More than 40,000 people have been killed in Gaza since then, according to the territory's Hamas-run health ministry.
A ceasefire deal agreed in November saw Hamas release 105 of the hostages in return for a week-long ceasefire and the freeing of some 240 Palestinian prisoners in Israeli jails. Israel says 111 hostages are still being held, 39 of whom are presumed dead.
In a recent joint statement, the US, Qatar and Egypt stated that they had presented a proposal for a ceasefire and hostage release deal that "narrows the gaps" between Israel and Hamas.
Israel has said any ceasefire deal would require the release of the remaining hostages taken to Gaza by militants during the 7 October attack on Israel. Some of the 251 hostages have already been released, while others are thought to have died in Gaza.
Relatives of hostages still in Gaza are calling the current negotiations as the "last chance" to get some of them out alive.
After 10 months of war and thousands of casualties, there is overwhelming pressure for a breakthrough.
A wider regional conflict, in the event of talks between Israel and Hamas collapsing completely, is a distinct possibility and is something all of those involved are fearful of.
The mediators said that the past two days of ceasefire discussions had been "serious, constructive and conducted in a positive atmosphere", external.
Technical teams are expected to continue working over the coming days on the details of how to implement the proposed terms before senior government officials meet again in Cairo, hoping to reach an agreement on the terms set out in Doha.
While the mediators' statement is clearly a positive development, there is still a long way to go before a ceasefire is agreed.
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