There was no official disclosure of the letter's contents, but the agency said it was likely a call to "return to the negotiating table without preconditions."
Netanyahu's letter was in response to a letter from Abbas last month in which the Palestinian leader called for a return to a 1967 agreement for two states and land swaps, the report said.
The Palestinians are also demanding Israel stop building settlements on disputed territories, including East Jerusalem.
Abbas and the Israeli envoy issued an optimistic joint statement after the letter exchange.
"Israel and the Palestinian Authority are committed to achieving peace and the sides hope that the exchange of letters between President Abbas and Prime Minister Netanyahu will further this goal," the release said.
Notable deaths of 2014 [PHOTOS]
Pakistan PM urges eradication of polio