Slovak President Ivan Gasparovic said late Tuesday that his country saw Medvedev's proposal for European security "as a means that should bring us closer together rather than separate us," RIA-Novosti reported.
Medvedev was visiting Slovakia on an official trip Tuesday and Wednesday.
A new security order in Europe was among the first foreign policy initiatives voiced by Medvedev after he assumed the presidency in May 2008. He first raised the idea in July 2008, and it took shape after the brief military conflict between Russia and Georgia the following month.
The proposed pact would require its signatories — countries or multinational organizations — not to strengthen their security at the expense of others, while giving each member the right to decide what constitutes a security threat from a foreign actor.
Earlier, only Germany had expressed a readiness to discuss the document, while other European governments and security blocs — NATO and the OSCE — have remained lukewarm.