The Quartet was formed in 2002 in Spain to assist in mediating an end to escalating violence in the Israeli-Palestinian conflict. It last met on the margins of the U.N. General Assembly in September.
But its results so far have been meagre, leading some analysts to dismiss it as an expensive club for diplomats.
Moscow had originally hoped to organise a full-scale international conference on the Middle East this year but the lack of progress on Israeli-Palestinian peace talks has forced Russia to settle instead for hosting a quartet meeting.
(Writing by Michael Stott)