Two days of talks were planned under the auspices of the Organisation for Security and Cooperation in Europe (OSCE), currently chaired by Lithuania.
"It took six years for both sides to sit at one table and to start official talks. That's the biggest achievement today," Lithuanian Foreign Minister Audronius Ažubalis told reporters after a first session, the Kyiv Post reported.
Ukraine, a country bordering Transnistria, follows the talks with utmost attention.
Ažubalis said the talks, which also involve envoys from Russia, Ukraine, the United States and the European Union, would first try to agree on the principles and procedures for further negotiations.
"We expect to start real work on the settlement of the Transnistria conflict," Moldovan Deputy Prime Minister Eugen Carpov told reporters before entering the talks.
Philip Remler, a former US diplomat who heads the OSCE's mission in Moldova, warned against expecting "miracles" from the two-day meeting.
Transnistria, a finger-like strip of land running down the eastern rim of Moldova, has been outside the control of the central government in Chisinau since a brief war after the collapse of the Soviet Union in 1992.
Moldovan authorities and EU officials say the breakaway region, home to about 550,000 mainly Russian-speaking people, has become a "black hole" for arms, drugs and people trafficking. Transnistria is not recognised by any state.
The Russian press quoted the ruler of Transnistria, Igor Smirnov, reiterating his invitation to Moscow to deploy medium-range Iskander missiles on the territory. Smirnov had invited Moscow already in February 2010 to deploy missiles in response to Romanian plans to host elements of a US anti-missile shield.
At the time, Russia refused. But this time Smirnov said that "Transnistria is ready to do what the purpose of keeping it separate from Moldova – to be a place d'armes for the defence of Russia".
Russia's relations with the US reached a low point after Washington signed an agreement with Romania to instal a missile shield there. They deteriorated even further last week after Moscow threatened to withdraw from the new START nuclear control arms deal with the US.
In a televised speech on 22 November, Russian President Dmitry Medvedev said that missiles and other weapons would be positioned in the country’s west and south to target US sites in Europe.
Russia may have to review its relations with NATO, including the Afghan issue, if the alliance keeps ignoring Medvedev’s ABM statement, the country’s envoy to NATO Dmitry Rogozin stated on Monday.
