Abkhazia and Georgia's other rebel region, South Ossetia, signed a mission exchange agreement in 2006 with Transdnestr.
"The representative offices opened in Sukhumi [Abkhazia] and Tiraspol [Transdenstr] will serve as an effective instrument in strengthening and developing brotherly and friendly relations between our republics," Abkhazia's deputy foreign minister said.
Transdnestrian Vice President Alexander Korolyov said negotiations were in progress on opening missions of some other states in Tiraspol.
The province, along with South Ossetia and Abkhazia, have stepped up their drive for self-rule since Kosovo's declaration of independence in mid-February, requesting that Russia, the UN and other organizations recognize their sovereignty.
Transdnestr proclaimed its independence from Moldova following a war in the early 1990s. Russia has deployed peacekeepers in the area since July 1992, and the negotiation process has been frozen since February 2006.