Hillary Clinton made the comments on Thursday following a meeting with Binyamin Netanyahu, the Israeli prime minister, in New York.
Clinton and Netanyahu ended the talks with a declaration of US "unshakable commitment to Israel's security and to peace in the region".
"The prime minister and the secretary agreed on the importance of continuing direct negotiations to achieve our goals," a joint statement said.
It did not mention, however, the issue of continued settlement construction on occupied Palestinian territories.
But Clinton said that the peace talks - which have hit an impasse over the settlement issue - could yet yield an independent Palestine living next to Israel "with secure and recognised borders that reflect subsequent developments and meet Israeli security requirements".
"Those requirements will be fully taken into account in any future peace agreement," the joint statement said.
Clinton stated that any future Palestinian state should be based on its 1967 borders with "agreed swaps" of territory, holding out the prospect that Israel might retain some of the occupied
West Bank in exchange for giving the Palestinians other Israeli territory.
AccordIng to Israeli officials, Netanyahu has pushed Clinton for new agreements on Israeli
security requirement in any eventual peace deal.
"The chances of reaching a peace agreement will be improved significantly by achieving comprehensive security understandings between Israel and the United States," Netanyahu said before Thursday's talks.
Israel wants a long-term military presence in the Jordan Valley along the eastern border of a future Palestinian state, as well as financial help to pay for security arrangements that would be necessary if a peace deal is achieved.
The talks in New York is the Obama administration's latest attempt to restart the direct peace talks that began in Washington on September 2 but were suspended by the Palestinians three weeks later when Netanyahu refused to extend a 10-month building freeze in West Bank settlements.
The deadlock over settlements appeared to deepen this week when Israel announced it was going to proceed with a new housing project in part of the West Bank that it annexed to Jerusalem 43 years ago.
The move underscored Palestinian concerns that Netanyahu's government will push ahead with settlements regardless of the impact on the peace process.