The Rwandan and CAR governments have accused ex-President François Bozizé of backing the rebels and plotting a coup, which he has denied.
UN peacekeepers have said the rebel advance has been halted.
Mr Bozize has been barred from a presidential election due on Sunday.
Russia has also sent “several hundred soldiers and heavy weapons” to the country to support the government, the AFP news agency quotes a CAR government spokesman as saying.
The spokesman, Ange Maxime Kazagui, said the Russian forces were invited as part of bilateral agreements, AFP reports.
The number of additional Rwandan soldiers deployed has not been given but the defence ministry said the operation was done “under existing bilateral agreements” with CAR.