Thomas-Greenfield made the comments at a news conference in Seoul, after being asked whether the United States was open to recognise the request by the Palestinian Authority to have full U.N. membership.
"We do not see that doing a resolution in the Security Council will necessarily get us to a place where we can find... a two-state solution moving forward," said Thomas-Greenfield.
She said U.S. President Joe Biden had categorically said that Washington supported a two-state solution and was working on the ground to get that in place as soon as possible.
The Palestinian Authority is expected to push the 15-member Security Council to vote, as early as Thursday, on a draft resolution recommending it become a full member of the world body, diplomats said. Security Council member Algeria circulated a draft text late on Tuesday.
A U.N. Security Council committee considering the application "was unable to make a unanimous recommendation" on whether it met the criteria, according to the committee report seen by Reuters on Tuesday.
An application to become a full U.N. member needs to be approved by the Security Council - where the United States can cast a veto - and then at least two-thirds of the 193-member General Assembly.
Little progress has been made on achieving Palestinian statehood since the signing of the Oslo Accords between Israel and the Palestinian Authority in the early 1990s.
Among the obstacles are expanding Israeli settlements, and Israel's U.N. Ambassador Gilad Erdan has said that the Palestinian Authority had not met the required criteria for statehood.
The Palestinian Authority, headed by President Mahmoud Abbas, exercises limited self-rule in the West Bank and is Israel's partner to the Oslo Accords. Hamas in 2007 ousted the Palestinian Authority from power in the Gaza Strip.
(Reporting by Josh Smith; Editing by Ed Davies and Miral Fahmy)
