U.S. President Barack Obama on Tuesday pledged commitment to the establishment of a sovereign Palestinian state and vowed to hold both Israel and the Palestinians accountable if either side takes actions that "undermine trust" during U.S.-mediated talks launched this week.

In a telephone conversation with Palestinian President Mahmoud Abbas, Obama welcomed the beginning of indirect Israeli-Palestinian peace negotiations and reiterated his strong support for the two-state solution.

The U.S. leader also urged both parties to "negotiate seriously and in good faith and to move from proximity talks to direct negotiations as soon as possible," the White House said.

Obama expressed during the conversation his appreciation for Abbas' recent gesture by appearing on Israeli television, and urged the president to prevent any acts of incitement or de-legitimization of Israel from the Palestinian people.

Earlier Tuesday, the Quartet of Middle East peace-brokers also urged Israel and the Palestinian Authority to pursue the proximity talks in "good faith" to prepare for full-fledged negotiations on settling their conflict.

The group welcomed the first round of talks held on Sunday with U.S. Middle East envoy George Mitchell shuttling between Jerusalem and Ramallah.

"These talks are a significant step toward direct, bilateral negotiations and comprehensive peace in the Middle East," the quartet said in a statement issued at UN headquarters in New York. The group is composed of the United Nations, the European Union, the United States and Russia.

The statement said that comprehensive peace is based on the establishment of an "independent and viable Palestinian state living side by side in peace and security with Israel and its neighbors."

"The quartet calls on all concerned to promote an atmosphere conducive to the talks and to act on the basis of previous agreements and obligations," the statement said.

The U.S. government said Sunday that the first round of talks ended with "serious and wide-ranging" compromises from both sides.

The two sides had taken "steps to create an atmosphere that is conducive to successful talks," State Department spokesman Philip Crowley said in a statement.