The assembly issued a unanimous declaration of proposals after a three-day meeting in Tirana, ahead of a landmark NATO summit in Warsaw in July.
"The challenge from Russia is real and serious," said Michael Turner, the US president of the assembly, which gathered around 250 lawmakers from the 28 member states.
The declaration expressed regret over "Russia's use of force against its neighbours and attempted intimidation of (NATO) Allies".
It said this had "left NATO no choice but to consider the prospect of aggressive Russian action against an Alliance member as a potential threat, and to adopt measured, proportionate responses".
The declaration urged NATO allies to "provide reassurance" to members who feel their security is under threat, especially on NATO's eastern and southern flanks.
In April, the NATO Russia Council (NRC) held its first meeting since June 2014 but the talks ended in "profound disagreements" over Ukraine and other issues, although alliance chief Jens Stoltenberg said at the time it was a useful exchange.
NATO has been undertaking a major military revamp to ensure a much quicker response in the event of a repeat of the Ukraine crisis.
The assembly said NATO should explore ways to "reduce tensions" with Moscow, while "addressing Russia's unacceptable violations of international norms".
It also called on NATO to strengthen conventional and nuclear deterrence, and to increase cooperation with European Union border agency Frontex over the migration crisis.
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