"The replacement of the CIS Collective Forces in the Georgian-Abkhazian conflict zone with European Union observers will not resolve the security problems in the region," Sergei Shamba told Zhang Yesui in the letter.
Shamba also informed Yesui of alleged Georgian acts of sabotage in Abkhazia and called on the UN Security Council to give an assessment of the situation. He said in August-October at least 14 acts of sabotage were committed in the Gali Region in Abkhazia, resulting in five dead and three wounded.
Russia handed control of buffer zones adjacent to Abkhazia and another Georgian rebel province, South Ossetia, over to EU and OSCE monitoring missions in Georgia on October 8, two days ahead of a deadline for Russian troops' withdrawal.
Russia recognized the rebel regions as independent states on August 26, two weeks after the end of a five-day war that began when Georgia attacked South Ossetia.
The two republics broke away from Georgia following the collapse of the Soviet Union in the early 1990s amid armed conflicts that claimed thousands of lives.
Earlier Monday, a senior Russian MP said the OSCE mission in the region was not coping with its tasks following the withdrawal of Russian troops.
"OSCE observers and peacekeepers are failing to cope with the situation in the region, and I fear that a new flare-up is possible," said Sergei Mironov, the speaker of the Russian parliament's upper house.
He said Georgia was still "interested in destabilizing the situation" in the region, and that international monitors were turning a blind eye.
UN Security Council consultations convened by Russia will take place in New York later on Monday to address Moscow's concerns over an alleged concentration of Georgian troops in the buffer zones adjacent to Abkhazia and South Ossetia.