The leaders met again Wednesday evening at the White House's old Family Dining Room for what was described as a working dinner.
When Abbas and Netanyahu meet Thursday, they will resume a process of formal negotiations that has been on intermittently and without success for almost 20 years, since the administration of President George H.W. Bush.
Obama offered no explanation of how the two sides could navigate around the first big threat to the talks: their disagreement over further Israeli settlement in the West Bank.
Netanyahu has indicated he is reluctant to extend a partial Israeli building moratorium that ends Sept. 26. Abbas has insisted that he will not sit at the table without a continuation of the freeze.