A top Israeli politician suggested Friday that there may be grounds for further peace negotiations between Israel and the Palestinians.

Foreign Minister Tzipi Livni said she was pleased with her meeting with Palestinian President Mahmoud Abbas on Friday at the World Economic Forum in Davos, Switzerland.

"We tried to explore any way which will promote the process" of talks based on two ideas, a Palestinian state and Israel's security, she said.

"We are creating this momentum … to put the train on the track and push it after that," Abbas told the Associated Press.

Abbas, Israeli Prime Minister Ehud Olmert and U.S. Secretary of State Condoleezza Rice are set to meet next month, which may give the process another boost.

On Thursday, Livni said a future Palestinian state "is achievable" and Israel's goal is peace. But Israel's security is vital, she said.

There have been several meetings between senior Israeli and Palestinian politicians to restart peace negotiations this week.

It's part of what appears to be a warming of the Israel-Palestinian relationship. Olmert and Abbas met in December, the first substantive face-to-face meeting in two years.

But any peace deal faces a major hurdle. Hamas, the elected government of the Palestinians, has not accepted Israel's right to exist, and members of Hamas and Fatah, the party Abbas heads, are battling in Palestinian areas.