The comments show how Turkey is increasingly playing both sides of the Russia-Ukraine conflict, standing apart from some other members of the North Atlantic Treaty Organization that are sending more weapons to Ukraine in the hope of stalling Moscow’s ongoing assault on the country’s east. While Western countries have moved to isolate Russia, Turkey has maintained an open line to Moscow, welcoming inflows of Russian money and facilitating two rounds of peace talks that ended without an agreement.

“Turkey is the only country I guess that can give a call to both parties and call them to the peace table. How can you do this if you send tens of thousands of weapons to one side?” Mr. Demir said in an interview with The Wall Street Journal.

Turkey’s Bayraktar TB-2 drones were instrumental in Ukraine’s initial resistance to the Russian invasion, blowing up military convoys and sinking warships. The drones’ success against Russian forces was celebrated by Ukrainians and helped improve Turkey’s standing in the West.

Turkey initially sold the TB-2 drones to Ukraine in 2019, and the two countries signed a new agreement for delivery of more of the aircraft, along with plans to jointly produce the drones, in February 2022.

A U.S. official said Turkey indicated in March that more of the drones would be forthcoming. Asked if Turkey was continuing to supply weapons including TB-2s to Ukraine, Mr. Demir said: “There are things going on, but I’m not in a position to say, but we are much more careful.”

Ukrainian and Turkish officials have declined to comment on any further deliveries of TB-2 drones. Baykar, the Turkish company that makes the drones, said earlier in June that it would donate one of the drones to Lithuania after a group of Lithuanians raised more than $6 million to buy one for Ukraine.

Mr. Demir said Turkey had no hesitation over selling other types of equipment, such as protective gear, to Ukraine.

“We have to be able to talk to both sides, someone should be close enough to both parties, to build trust,” he said.

“Our priority is to make sure that peace prevails,” said Mr. Demir.

Mr. Demir’s comments came as Ukrainian officials have expressed concern that Turkey is gradually shifting its position toward Russia, after initially taking concrete steps to support Ukraine’s war effort in the early days of the invasion.

In recent days, Ukraine has accused Turkey of buying stolen wheat from Russia. A senior Ukrainian official said Ukraine is asking itself: “‘Is Turkey switching sides?”

“Turkey’s interests come first for Turkey,” the senior Ukrainian official said.

A Turkish official said the concerns about the country shifting its position on the conflict were “baseless.”

“We stand by Ukraine in political, humanitarian and other fields,” the official said.

The official also said Turkey is processing information Ukraine had provided about the allegedly stolen grain. Russian authorities provided documents saying the cargo had originated in Russia, the official said.

“It is technically very difficult to determine the geographic origin of grain,” the official said.

Mr. Erdogan has tried to maintain good relations with both Ukraine and Russia—two Black Sea neighbors that are major sources of commodities for Turkey. He has made moves that have pleased and displeased both sides.

Though Turkey didn’t impose economic sanctions against Russia, the country shut off access to the Black Sea for Russian warships and closed Turkish airspace to certain Russian military flights from Syria following a request from Ukraine.

Ukrainian officials initially welcomed the Turkish government’s role as a facilitator of peace talks, saying that Turkey was a more neutral site for the negotiations than their original location in Belarus, a Russian ally that aided in the assault on Ukraine.

In recent weeks, Turkey has also sought to broker a deal that would help export grain and other vital food products from Ukraine. As much as 20 million metric tons of grain has been trapped in Ukraine as a result of the Russian invasion, raising fears of a global food crisis.

Turkey broke with the Western consensus on the Ukraine crisis when Mr. Erdogan decided in May to block Sweden and Finland’s application to join NATO over concerns about the presence of Kurdish militants in the two countries. The three countries are continuing negotiations to try to resolve the dispute this week.

Mr. Erdogan has long had an unusual partnership with Russia’s President

Vladimir Putin,

authorizing purchases of Russian weapons while also sending Turkish forces to fight proxy wars against Russia in Syria and Libya.

In recent weeks, Mr. Erdogan has also called for a new military operation against Kurdish militants in Syria, an action that would likely require Russian approval because of the presence of Russian soldiers in the specific areas of Syria that Mr. Erdogan says it plans to attack.

The battlefield dynamic has also shifted in Ukraine, with Russia making gains in the east after failing to achieve its early objectives.

“As it becomes clear that there may not be an immediate victory, they’re starting to become more cautious,” said Asli Aydintasbas, a senior policy fellow with the European Council on Foreign relations.

“Turkey increasingly characterizes this as a contest between the West and Russia and does not want to get caught in that. The logic of neutrality is stronger in the country now than three or four months ago,” she said.

—Elvan Kivilcim contributed to this article.

Write to Jared Malsin at jared.malsin@wsj.com