The two leaders have not had a substantive meeting in several years, and the direct talks proposed by Russia would have represented a breakthrough in peace efforts.
Palestinian Authority president Mahmoud Abbas and Israeli prime minister Binyamin Netanyahu have both expressed a readiness for direct talks.
And speaking in Poland this week, Mr Abbas said he had accepted an invitation from Russian president Vladimir Putin for talks in Moscow on September 9.
But he says Israel has asked to delay the meeting until an unspecified later date.
"However, I am prepared to attend tomorrow or at a time agreed upon, because this dialogue between us and the Israelis is of great importance to me, whether it be in Moscow or any other place, because dialogue is the only way to reach peace for the Palestinian nation and Israel."
Speaking in the Netherlands, Israel's Prime Minister Binyamin Netanyahu has reiterated he is ready for direct talks with Mr Abbas, also known by the name Abu Mazen.
Mr Netanyahu says he is open when it comes to the location, but he maintains he will not tolerate preconditions, including the release of prisoners.
"If Abu Mazen is ready to meet, without preconditions, for direct talks, I am ready at any time. I've been calling on him to do so for nearly seven years. If he agrees to do this, there will be a meeting."
Mr Netanyahu's visit to the Netherlands has met with protests, though.
Demonstrators in The Hague have demanded the International Criminal Court based there put the leader on trial for alleged war crimes.
"If our own government is not going to do something about it, then we as people, we as citizens of the Netherlands and elsewhere in the world, should have a say and should make a stand, and that is why I'm here today."
Israel has reportedly agreed to let the court send a delegation to Israel and the Palestinian territories to examine allegations its military broke the laws of war during the 2014 Gaza War.
A foreign ministry spokesman has told Al Jazeera Israel has agreed to the visit in principle.
Human-rights groups have questioned the credibility of Israeli investigations into alleged war crimes.