According to the report, the American and Palestinian presidents discussed recent developments in the Middle East and the peace negotiations between Israel and the Palestinians following Obama's meeting with Prime Minister Benjamin Netanyahu earlier this week.
Abu Rudeina added that Obama promised to work towards the establishment of a Palestinian state, which would live in peace and security alongside Israel.
Obama and Netanyahu want direct talks soon on a Middle East peace treaty, but Abbas appears wary of walking into a trap.
The Palestinians insist on keeping Israel at arm's length until it makes certain things clear – namely, what size and shape of Palestinian state is Netanyahu prepared to consider, and will its Jordan Valley be free of Israeli troops?
Israel says the current "proximity talks" are wasting time.
"What we want to see finally is one thing. We want President Abbas to grasp my hand ... to shake it, sit down and negotiate a final settlement of peace," Netanyahu said on Wednesday.
Obama's endorsement of that goal at the White House meeting on Tuesday was a sign that moving swiftly to direct negotiations well before September is vital to keeping the process alive.
Chief Palestinian negotiator Saeb Erekat said Wednesday that "the key to direct talks is in the hand of Prime Minister Netanyahu. The minute he announces a (total) settlement freeze, the minute he announces the resumption of final status (talks) where we left them in December 2008, we will have direct talks".
Reuters contributed to this report
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