"In the letter, President Barack Obama warned president Mahmud Abbas that his refusal to enter into direct negotiations with Israel next month will have consequences for American-Palestinian relations," the official said.
The 16-point letter had a "carrot-and-stick approach," he added.
Obama stressed "it is high time to resume direct negotiations with Israel" and told Abbas that Israeli Prime Minister Benjamin Netanyahu "is ready to resume direct negotiations."
The letter warned that "Obama will absolutely not accept the rejection of his recommendation to move to direct negotiations and that there will be consequences for such a rejection in the form of a lack of trust in president Abbas and the Palestinian side," the official said.
Obama pledged that his administration would work to extend a partial Israeli moratorium on Jewish settlements due to expire in September if Abbas resumes direct negotiations, he added.
"But in case of a refusal its assistance on that issue will be very limited," he said, quoting from the letter in Arabic.
Chief Palestinian negotiator Saeb Erakat confirmed to AFP that Abbas received a letter from the US president on July 16.
"The president received on July 16 a letter from Obama in which he calls on the Palestinians to enter into direct negotiations and that these negotiations will lead to the creation of an independent Palestinian state," Erakat said.
In the letter Obama "assured Abbas that the US administration will strive to put an end to (Jewish) settlements if direct peace talks go underway but that its role would be less if this does not happen," Erakat said.
The revelation comes after the Arab League agreed in principle on Thursday to the resumption of direct Palestinian-Israeli peace talks, stressing however that Abbas had the final word on whey they should start.
The Palestinian official who declined to be named said Obama expects direct peace talks to begin at the onset of August and to address thorny issues such as borders and Israeli-annexed east Jerusalem.
Abbas, who is holding US-brokered indirect talks with Israel, has conditioned going into face-to-face talks with Israeli Prime Minister Benjamin Netanyahu on a raft of demands rejected by Israel.
He wants a complete end to settlement construction in east Jerusalem and the West Bank, which Israel occupied in 1967, and has said negotiations on a Palestinian state's borders must be based on the pre-1967 borders.
He has threatened to turn to the UN Security Council if there is no progress on his demands by September, when the four-month indirect talks with Israel are due to end.
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