Though Abbas had backed off on a demand for a full halt to Israeli settlement building on occupied land before any talks, he has spoken of US assurances that Israel will not do anything "provocative" to derail the negotiations.
Obama's statement appeared in part aimed at satisfying Abba's fears that Israel's right-leaning government might announce further expansion of Israeli housing in and around Jerusalem. The settlement issue has strained ties between Washington and close ally Israel.
The White House said Obama also urged Abbas to "do everything he can to prevent acts of incitement or delegitimisation of Israel."
Abbas is weakened politically by Hama's control of the Gaza Strip while he only governs in the West Bank.
Obama, who has stressed his commitment to Israel's security, also reiterated his support for establishment of an "independent, viable Palestinian state living in peace and security with Israel."
Benjamin Netanyahu, the Israeli prime minister, who heads a coalition government dominated by pro-settler parties, has rejected a total freeze on construction of Jewish settlements in occupied territory.
But no new Israeli housing projects in East Jerusalem have been approved since March, raising speculation Netanyahu has imposed a de facto moratorium that could keep talks ticking while avoiding a showdown with his far-right coalition partners.
The US plans for indirect talks were halted in March, when Israel angered Washington and the Palestinians by announcing during a visit by Joe Biden, the US vice president, a project to build 1,600 new homes in the Ramat Shlomo settlement.