The comments come nearly one month after direct peace talks between the two sides resumed after a three-year stalemate.
"There is nothing at all that prevents a meeting with Prime Minister Netanyahu at the right time for us to meet or at a time we need to meet," Abbas said in Ramallah at a press conference with visiting French Foreign Minister Laurent Fabius.
The Palestinians and Israel have held three rounds of talks since negotiations began at the end of July. They have been limited, however, to negotiating teams on both sides.
Abbas said the unrest in neighboring Arab countries did not distract him from taking the decision to launch negotiations.
"When the negotiations opportunity opened, we took it without looking at what was going on in the region around us," he said.
Fabius said that a peace agreement between Israel and the Palestinians would improve stability and security in the region.
"The crisis in the region could be an obstacle to negotiations," he said. "It is therefore important to move forward with negotiations because this will be excellent for peace and stability in the region."
He said France supports the peace process and that despite other tensions in the Middle East, "the Israeli-Palestinian conflict remains the crux of the matter and should be resolved peacefully."
Abbas reiterated the Palestinian commitment toward peace with Israel and expressed hope that Israel will also show similar intentions by halting settlements and releasing prisoners.
The French minister urged Israel to stop settlement activities, which he described as illegal under international law and do not help confidence building between the two sides.
Fabius arrived in Ramallah on a two-day visit to the Palestinian areas and Israel. He is expected to hold talks with Israeli officials on Sunday.
He had earlier met Palestinian Prime Minister-designate Rami Hamdallah and signed two agreements worth 19 million euros, including 9 million euros in budget support.
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