BRATISLAVA, Slovakia—Montenegro's prime minister said he hopes the country will get an invitation this fall to join the North Atlantic Treaty Organization despite new tensions between the West and Russia, which views NATO's eastward enlargement as a strategic threat.

After five years of talks, Montenegro, which emerged largely unscathed from the war following the breakup of Yugoslavia in the 1990s and has a population of 650,000 people, could become the first new NATO member since Croatia and Albania joined the alliance in...