"I thank President Abbas for the progress we made today and for the issues we have discussed," Xinhua quoted Kerry as saying in a joint press conference with chief Palestinian negotiator Saeb Erekat after meeting Abbas.
Kerry's Saturday meeting with Abbas in Ramallah was the second in less than 24 hours.
"We are seriously working with a commitment to trying to resolve this conflict that has been going on for many years. As Saeb (Erekat) said we are not there yet, I say we are making progress," said Kerry, adding that he remained hopeful.
He also said that this progress provided all sides with the possibilities of finding a framework agreement which would lay out the framework to guide the negotiations.
Kerry said that in this week his teams will continue to work to formulate the foundation in the framework for the progress needed in order for him to come back and take the next step.
However, Erekat denied that the US has presented to the Palestinians any official written document or plan of a framework agreement, adding "all what was presented so far is ideas that are still under discussions and debates between the two sides".
"Nothing has been presented to us. We are still in the status of exchanging views and ideas," Erekat told reporters, adding that Kerry will return to the region within the coming days "to continue our discussions."
In comparison to Kerry's optimism, Erekat said that negotiations between Israel and Palestine face difficulties, adding "the job is not done yet."
Since March 2013, Kerry has been exerting efforts between Israel and the Palestinians to help the two sides resolve their differences and reach a peace agreement. Although the talks have been going since late July 2013, no progress has so far been achieved.
Meanwhile, a well-informed Palestinian source said that Kerry had exerted heavy pressure on Abbas to accept the proposal of signing on a transitional peace framework agreement that tackles the outlines of the permanent status talks.
The source said that Abbas conditioned signing on the framework agreement with the full freeze of all settlement activities during the transitional period of the framework agreement, adding "Kerry didn't present any written plan and new ideas in relation to borders and security."
Nabil Abu Rdineh, an aide to Abbas, said in a statement that President Abbas reiterated to Kerry in the two meetings held Friday and Saturday that the Palestinians won't accept less than an independent Palestinian state on 1967 territories with east Jerusalem as its capital.
"President Abbas rejects all transitional, partial and temporary solutions," said Abu Rdineh, adding "President Abbas and Kerry agreed to keep meetings and contacts in the coming weeks."