The small Balkan country of Macedonia is turning into an unexpected stage for tension between Moscow and the West.

A year and a half after antigovernment protests broke out in the Ukrainian capital of Kiev, similar scenes are playing out on the streets of Skopje, Macedonia: Tens of thousands of protesters have swarmed the city’s center in recent weeks, angered over excerpts from illegal wiretaps that activists say expose corruption and a gross abuse of power in Prime Minister Nikola Gruevski’s government.

The crisis intensified in May after a police raid in Kumanovo, a town with a history of ethnic tension, left 22 people dead, including police. Authorities said a gunbattle broke out with ethnic Albanian insurgents, but the opposition accuses the government of instigating the clash to create a diversion from the wiretap revelations.

Protesters are demanding that stalled talks for Macedonia to join the European Union be revived and have vowed to stay camped outside government buildings until the country’s leaders resign.

Officials in Moscow say they see another hand at work in the former Yugoslav republic: Western powers. “Events in Macedonia are being crudely manipulated from the outside,” Russian Foreign Minister Sergei Lavrov told the parliament in Moscow in May.

On a visit to the Serbian capital of Belgrade on May 15, Mr. Lavrov suggested the West’s likely motives: Macedonia, which is heavily reliant on Russia natural gas, has refused to support Western economic sanctions against Moscow imposed over the Ukraine crisis.

Macedonia’s government, he also noted, is backing Russia’s Turkish Stream gas-pipeline project—its latest effort to bypass Ukraine to deliver gas into southeast Europe through Turkey, Greece and possibly Macedonia. The proposal competes with EU efforts to reduce the bloc’s dependency on Russian gas, including a now-aborted project to link Europe with supplies from Azerbaijan.

“We can’t help feeling that there is some kind of connection between the two events,” Mr. Lavrov said of the demonstrations and the Macedonian government’s siding with the Kremlin on the sanctions and pipeline fronts.

Russia’s interest in the Balkan country has never been as deep as with Macedonia’s northern neighbor, Serbia, another former Yugoslav republic with which Russians share an Orthodox faith and long-standing cultural ties.

But amid the Turkish Stream project and the protests that led to the ouster of Ukraine’s Kremlin-backed president, Viktor Yanukovych, last year, Macedonia’s unrest has taken on greater geopolitical importance in Moscow.

That shift has become increasingly visible. Russian flags were spotted at a recent pro-Gruevski rally. The Russian Embassy in Skopje has beefed up its staff by 25%, said Erwan Fouéré, a former EU envoy to Macedonia.

Last month, Macedonia’s President Gjorge Ivanov attended President Vladimir Putin’s Victory Day military parade to mark the 70th anniversary of the defeat of Nazi Germany, an event snubbed by most Western leaders.

The EU—fearful the turmoil could ripple across the Balkans—has sought to mediate, and is “very actively engaged” in finding a political resolution, a European Commission spokeswoman said.

At a 12-hour meeting in Strasbourg, France, on May 19, Mr. Gruevski and the main opposition leader, Zoran Zaev, agreed to negotiations. Another EU-mediated session is scheduled in Skopje this week.

Mr. Zaev first accused Mr. Gruevski’s government of using illegal wiretaps several months ago, alleging that it had monitored some 20,000 people, including 100 journalists, in recent years, in a bid to tighten its grip on the media, interfere in judicial investigations and, in some cases, rig elections. His party has since released excerpts of the alleged surveillance tapes—which he says he received from a whistleblower—on a weekly basis.

Mr. Gruevski has denied the allegations and said the recordings were doctored in a bid to destabilize his government. He has agreed to allow parliament to investigate the wiretaps.

Dmitri Trenin, director of the Moscow Carnegie Center think tank, said that while Kremlin officials probably don’t believe the West instigated the unrest in Macedonia, they suspect Western capitals of exploiting it to pressure Macedonia into withdrawing its support for the Turkish Stream project.

The Russians “know that Macedonia has never been stable,” Mr. Trenin said. “So the thinking is that the current crisis has something to do with the attempts to check Russia’s plans and influence in the Balkans.”

Some, though, say Europe’s stalled effort to bring Macedonia closer into its fold has created an opening for Moscow.

The North Atlantic Treaty Organization mapped out a plan in the late 1990s for Macedonia to join NATO, and the country applied for European Union membership a decade ago.

But the Greek government has blocked both moves because of a dispute over Macedonia’s name, which Greece says belongs to its own northern region.

“The leverage of the EU on Macedonia is diminishing. The certainty that EU membership will happen is now lost. And young people are living in worse conditions than their parents and in far worse than their grandparents, during Yugoslav times,” said Dusan Reljic from the German Institute for International and Security Affairs, a think tank. “So the government in Skopje is looking for alternatives—in China, in Russia, in Turkey or Azerbaijan. There is a plurality of external influences appearing.”

Nikola Dimitrov, a former Macedonian ambassador to Washington and the Netherlands, said EU neglect had left Macedonia “too long at the mercy of Greece.”

“It’s a question of credibility. If the EU can’t make a difference in Macedonia—a country of two million, surrounded by EU states—then how can we even think of Ukraine or Mali?” he said.