Speaking in London at the Royal Institute of International Affairs, he said: "We are confident that Poland's accession to Nato will lead to a projection of stability and security into areas stretching beyond our eastern frontier."
Poland and Russia have had a historically fraught relationship, with major Polish uprisings against tsarist rule in the 19th century and a war in 1920-21. The Soviet Union invaded Poland in 1939 from the east shortly after the Nazi invasion from the West, and then imposed Communism on the Poles after 1944.
But Mr Kwasniewski said Polish-Russian relations were developing in a promising fashion. "The Poles have reached the conclusion that security to them means first of all Poland's membership in the North Atlantic alliance," he said.
Poland is one of three or four former Communist countries widely expected to be invited to join Nato next year and become full members by 1999. The others are the Czech Republic, Hungary and Slovenia.
Nato officials say that Russia, despite public opposition to the Atlantic alliance's enlargement, has privately resigned itself to expansion, on condition that Nato does not move nuclear weapons or military infrastructure into new member- states. Nato has sought to allay Russian suspicions by proposing a charter that would set the terms of a close relationship between Moscow and the alliance in the post-Cold War age.
British officials said they anticipated few problems in Poland's accession talks with Nato, but added that it might prove more difficult for Poland to join the European Union by 2000. This date was mentioned in a speech that President Jacques Chirac of France recently gave in Warsaw, but European Commission officials later described 2002 as a more realistic target.