Russian President Putin and Belarusian President Lukashenko on Friday had their first conversation since reports 33 Russians were arrested on July 29 in Minsk.
Belarusian authorities said they had detained the "mercenary" group last week on charges of planning "mass protests" ahead of the presidential election.
But Russia has denied claims, adding that the 33 Russians were not linked to activists opposing Lukashenko.
The Kremlin has demanded their quick release, saying they stayed in Belarus after missing their connecting flight to another country.
According to Moscow, when the two leaders spoke on the phone, they "voiced confidence that the situation will be settled in the spirit of mutual understanding typical for cooperation between the two countries."
The Kremlin added that "Russia is interested in the preservation of a stable domestic political situation in Belarus and calm atmosphere at the forthcoming presidential election."
Election threatens relationship
Lukashenko has described recent anti-government protests as part of a "hybrid war" waged by enemies; he said that the West, Ukraine and even Russia, could all be interested in destabilising his government.
Dmitry Medvedev, deputy head of Russia's Security Council, said without naming Lukashenko, that this and the arrests were Belarus' attempt to paint Russia as an enemy, ahead of the elections.
He warned this week that the recent actions from Minsk would have "sad consequences" for bilateral ties. The Belarussian leader dismissed the threat. "Don't try to scare us with consequences," he said.
The arrests marks a new low point in relations between the two countries. Belarus is tightly linked to Russia, and the two nations share an economic zone and are military allies but this cooperation has recently been under strain.
Nearly 30 years since splitting from the Soviet Union, unresolved questions about national identity underpin the upcoming presidential election.
The end of the Warsaw Pact alliance left Belarus squeezed between Russia to the East and the European Union to the West. How to manage this situation became a defining question, a problem that finds illustration in the different flags flown around Minsk.
The red and white flags of the opposition have anti-Moscow connotations: they refer to the pre-soviet era — when Belarus was briefly independent. The official flag is red and green, as it was during the time of the USSR.
First with Boris Yeltsin and then with Vladimir Putin, the early years of President Lukashenko's rule were marked by warm ties with Russia. Certainly, it was an alliance of necessity — Belarus depends on Moscow for fuel and trade, but it went further, with talk of a union between the two states.
The relationship between Minsk and Moscow has been cooling since last year, possibly because Lukashenko was worried that the union plan was beginning to look like a takeover.
He has recently sought to spread his options by strengthening ties with China and the United States.
A meeting with US Secretary of State Mike Pompeo last year was seen as a potential new opening for Belarus.
Still, Washington has since been highly critical of the arrest of political opponents during the current election campaign and the refusal of Minsk to allow international observers to monitor the poll.
Lukashenko's support base is in rural Belarus and his most recent speeches have sought to unite the country around overtly nationalistic rhetoric.
But it remains to be seen whether he will be able to contain the tensions that his authoritarian style of government generates, particularly among urban populations more attracted to economic liberalism.
He warned political opponents this week that authorities won't allow any unsanctioned demonstrations after the election.