“We can’t speak now about what happened,” he told a joint press conference with UN chief Ban Ki-moon at his headquarters in the West Bank city of Ramallah.
At the request of Washington, Israel and the Palestinians have so far maintained a strict news blackout on the US-brokered talks.
“We discussed the issues which are always on the table: borders, Jerusalem, settlements,” Abbas said.
“Until now we didn’t speak about what happened (in the talks) and when there is something we shall tell you.”
Ban, who arrived from Jordan, called upon both sides to avoid actions which could disrupt the fragile negotiations, which resumed on Wednesday in Jerusalem after a three-year hiatus.
In Amman earlier, he urged Israelis and Palestinians to show “patience” to give the peace talks a chance of success, Jordan’s state-run Petra news agency reported.
He “called on the Israelis and the Palestinians to have patience and do all that they can for the success of their negotiations and achieve the needed progress with the help of the international community.”
Israeli and Palestinian negotiators met for around five hours on Wednesday in a new round of direct peace talks, which broke down in September 2010 in a bitter row over Jewish settlements.
The United States has been prodding the sides for several months to return to the negotiating table.
Ban, who is to meet both Israel’s prime minister and president on Friday, said he was pleased “to visit the state of Palestine.”
The UN General Assembly on November 29 upgraded Palestine to the status of non-member observer state by a vote of 138 votes in favour, nine against and 41 abstentions.
The Palestinian Authority now uses the “State of Palestine” in diplomatic correspondence and has issued official stamps for the purpose.
Israel maintains that Palestinian statehood can only be obtained through a negotiated settlement of their decades-old conflict.
In Jordan, Ban met with King Abdullah II to discuss the peace process and the hundreds of thousands of Syrian refugees who have fled to the kingdom, the palace said.
He “stressed he is committed to working with the international community in order to increase aid to Jordan and help minimize the burden of dealing with the Syrian refugees,” it said in a statement.
Ban is on a tour of Jordan, Israel and Palestine aimed at buttressing the peace process.