"We are also ready to engage with key regional countries in order to consolidate collective efforts and to hold Quartet meetings with their participation," Nebenzia told a UN Security Council meeting.
Nebenzia added that Russia will continue pursuing dialogue with nations in the Middle East and the League of Arab States.
The Middle East Quartet on Israeli-Palestinian settlement (Russia, US, EU, UN) may hold a teleconference in the coming week, a source said on Wednesday.
"This contact could take place in the next few days, perhaps by the end of the week," the source said, adding, however, that there was no definitive agreement on the talks.
The previous talks in the format took place on 26 March.