Jordan is hosting two peace talks between Israel and Palestine on Tuesday.
The Quartet envoys would participate in the first meeting between Israeli and Palestinian negotiators while the second one would be held only between Israeli and Palestinian representatives, Jordan's Foreign Minister Nasser Judeh said.
Jordan's initiative is aimed at setting up a common agenda to bring about peace in the region. Several lives were lost in the ongoing land dispute between the nations, which started in 1920.
The Quartet, which the U.N. set up in 2002 to settle the Israel-Palestine dispute, has said it wants both the parties to set a proposal within three months. The group hopes to strike a mutually acceptable agreement between Israel and Palestine by the end of 2012.
The U.S. welcomed Jordan's initiative. "We are hopeful that this direct exchange can help move us forward on the pathway proposed by the Quartet. As the President and I have said before, the need for a lasting peace is more urgent than ever. The status quo is not sustainable and the parties must act boldly to advance the cause of peace," U.S. Secretary of State Hillary Rodham Clinton said in a statement.