Peace talks stalled
All sides in the Annapolis talks have said the year-end deadline for a deal will not be met.
The talks have been symied by ongoing violence, disputes over illegal Jewish settlement-building on Palestinian land and the future of Jerusalem, which both sides claim as a future capital.
In addition, Bush leaves office on January 20, when Barack Obama, the US president-elect, will take over as president.
Churkin said that a new UN meeting was essential as the Middle East conflict was "now at quite a delicate and important stage".
"It's been a long time since the security council has approved any kind of joint reaction [or] joint signal on the matter of the Middle East peace process," he said.
The so-called Middle East quartet of peace negotiators - comprised of the European Union, Russia, the UN and the US - are also due to meet at the UN headquarters in New York City on Monday and will in addition hold talks with Arab foreign ministers.