Abbas "will have an important meeting with President Francois Hollande to discuss convening an international peace conference in accordance with the French initiative," Palestinian presidential spokesman Nabil Abu Rudeina told AFP.
The Palestinian leader will travel to France on April 15, before heading to Moscow to meet Russian President Vladimir Putin and discuss "the evolution of the political situation in Palestine and the region", he said.
Abu Rudeina said Abbas would also travel to Berlin for a meeting with German Chancellor Angela Merkel before flying to New York to attend meetings at the United Nations, but he did not provide exact dates.
France launched an effort earlier this year to host an international conference to revive peace talks between Israeli and Palestinian leaders.
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It initially vowed to recognise a Palestinian state if talks failed, but French Foreign Minister Jean-Marc Ayrault later said the recognition would not be automatic.
"France plays an important role in efforts to establish a fair, comprehensive and durable peace in accordance with international resolutions," Abu Rudeina said.
The French initiative comes amid a wave of violence since October that has killed 200 Palestinians and 28 Israelis.
Most of the Palestinians were killed while carrying out knife, gun or car-ramming attacks, according to the Israeli authorities.
Others were shot dead during protests and clashes, while some were killed in Israeli air raids in the Gaza Strip.