White House spokesman John Kirby said Washington hoped Hamas would release more Americans.
The United States believes Hamas is holding between eight and nine Americans hostage after the release of a four-year-old girl.
On Israel's intention to resume fighting in Gaza after the current truce expires, Kirby said there were currently more Gazans in the south and therefore there was an additional burden on Israel to protect their lives in any operation.
He explained that his country is working on the possibility of extending the current truce.
CIA Director William Burns arrived in Qatar on Tuesday. The talks were attended by David Parnia, head of Israel's Mossad intelligence agency, the head of Egypt's intelligence service, Major General Abbas Kamel, and senior officials from Qatar.
The Israeli delegation led by the head of the Mossad presented during talks in Doha with the heads of the intelligence services of the United States, Egypt and Qatar a proposal for a long ceasefire, but under specific conditions, the Israel Broadcasting Corporation said.
What is proposed?
The Israel Broadcasting Corporation said the delegation demanded the release of all Israeli detainees in exchange for a long ceasefire and the release of a large number of Palestinian prisoners.
Our correspondent in Jerusalem quoted Israeli sources as saying that the government's instructions to the negotiating delegation in Doha are first to release the remaining mothers and children, and then we can talk about new deals.
Egyptian officials speak out
The Wall Street Journal quoted Egyptian officials as saying the aim of the Doha talks "is to move the discussions beyond the current arrangement of extending the initial four-day agreement by one day for every 10 hostages handed over by Hamas."
"The talks are now focused on how to free the elderly, corpses and soldiers once all the women and children are out," the newspaper said.
Senior Egyptian officials said Qatari and Egyptian mediators were pushing for a longer cessation of hostilities, hoping it would develop into a permanent ceasefire.
In addition to allowing more hostages to be released, more extensions could give Israel more time to define and prepare for a postwar political settlement in the Strip, according to the Wall Street Journal.
A senior Egyptian official told the newspaper: "We are trying to build trust and goodwill to open the door to long-term peace."
"It's a distant opportunity, but so far both sides have refrained from seeking a military advantage during the truce period, which gives us hope that this can be done," he said.