BRATISLAVA—Slovakia, a NATO member that has called itself part of the “core of the European Union,” may talk positively about its Western orientation, but its actions recently suggest an increasingly closer alignment to Russia and its interests in Europe. Many observers point to the junior partner in its coalition government, the Slovak National Party, or SNS, as the reason why. The party’s nationalist, euroskeptic leader, Andrej Danko, the speaker of the Slovak parliament, has visited Moscow twice in the past eight months.

Earlier this month, Slovakia’s Defense Ministry, which is headed by a member of the SNS, postponed a long-awaited decision to replace Slovakia’s fleet of aging Russian-made MiG-29s with Swedish Gripen fighter jets or U.S.-made F-16s. The move was widely criticized, including by members of the ministry’s own leadership as well as partners in the coalition government. Defense Minister Peter Gajdos had put the years-long talks with Gripen’s manufacturer, Saab, on hold and invited other bids. ...