On the day after Brittney Griner was sentenced to a Russian penal colony, the top diplomats of the United States and Russia said on Friday that their governments were ready to negotiate for the release of both the American basketball star and Paul N. Whelan, who is also imprisoned by Russia.

The diplomats, Secretary of State Antony J. Blinken and Foreign Minister Sergey Lavrov of Russia, said in separate news conferences that the negotiations would be conducted through a channel established earlier by their two presidents.

But in a possible indication of how tense the relations between the two countries are, the two men made their comments after sitting close to each other — but not talking — during a meeting of foreign ministers from East Asia and partner countries.

On Thursday Ms. Griner received a sentence of nine years from a Russian judge. American officials have said that she was “wrongfully detained” and that her trial was politically motivated, as relations between the two countries remain strained over Russia’s war in Ukraine.

The Biden administration has offered to free Viktor Bout, an imprisoned Russian arms dealer, in exchange for Ms. Griner and Mr. Whelan, a former U.S. Marine who was convicted by a court in Moscow of espionage charges in 2020, according to people familiar with the proposal.

After the meeting on Friday, Mr. Lavrov took the opportunity to needle Mr. Blinken for not making any effort to talk to him.

“Today, there was only one person between us at the table,” Mr. Lavrov said at a news conference broadcast by the Foreign Ministry. “I didn’t see him trying to catch me.”

When asked about Mr. Lavrov’s remarks and Ms. Griner’s conviction, Mr. Blinken stressed that discussions would move forward through previously established channels.

“We put forward, as you know, a substantial proposal that Russia should engage with us on,” Mr. Blinken said. “And what Foreign Minister Lavrov said this morning, and said publicly, is that they are prepared to engage through channels we’ve established to do just that, and we’ll be pursuing it.”

Russian officials have criticized the United States for what they described as negotiating the prisoner exchange in public.

The Kremlin’s spokesman, Dmitri S. Peskov, renewed that criticism on Friday. “These swaps will never happen if we start discussing any nuances of the exchange in the press,” Mr. Peskov told reporters in Moscow.

Despite sending signals that a potential exchange is possible, Russian officials have insisted that legal due process must be completed first. After hearing the verdict on Thursday, Ms. Griner’s lawyers said they would appeal the sentence, which would delay the start of her time in a penal colony.

In another crucial meeting with possible implications for the war in Ukraine, President Vladimir V. Putin of Russia and his Turkish counterpart, Recep Tayyip Erdogan, held their second face-to-face conversation in less than three weeks in the Russian Black Sea resort town of Sochi on Friday.

Mr. Erdogan has emerged as an important mediator between Ukraine and Russia, which is probing for ways to break out of the economic and political isolation imposed by the West over its invasion of Ukraine. Turkey, a NATO member and a long-frustrated E.U. applicant, proved instrumental in forging an agreement between the two warring countries to restart Ukrainian grain shipments through the Black Sea.

In brief remarks before the leaders’ discussion began, Mr. Putin thanked Mr. Erdogan for Turkey’s role in mediating a deal to export Ukrainian grain that also allowed for shipments of Russian grain and fertilizer exports. There was a heavy emphasis on economic matters, with Mr. Putin expressing hope that the talks would bring enhanced trade and economic ties.

Mr. Erdogan said that the steps taken on issues like energy, grain, the Black Sea and transportation were examples of the important role that Turkey and Russia play in the region.

Mr. Erdogan is treading a fine line to retain the ability to talk to both Russia, NATO’s foe, and to Western members of the alliance. Turkey has held to its refusal to join Western sanctions against Russia, irking its NATO allies, but Mr. Erdogan, in a crucial move, also eased his initial objections to Sweden and Finland joining the alliance as a bulwark against Russian aggression.

Russia is a critical supplier of energy to Turkey, providing a quarter of the country’s crude imports and almost half of its natural gas purchases last year.

For its part, Turkey is becoming an important transshipment point for goods headed to Russia, now that many Western freight companies no longer handle Russia-bound shipments for fear of defying sanctions, the Turkish newspaper Dunya reported on Thursday.

But stark differences remain between the two leaders.

Their countries have backed opposing sides in the civil war in Syria, Turkey’s neighbor. The Kremlin has expended blood and treasure to shore up President Bashar al-Assad, while Turkey, which has absorbed more than 3.7 million Syrian war refugees, supports an opposing rebel faction and is threatening a new military offensive in Syria’s north. They have also been involved on opposing sides in the border dispute between Azerbaijan and Armenia, which erupted into war in 2020.

Their relations regarding weapons are also complex. In recent years, Turkey defied its NATO partners to buy Russian antiaircraft missiles. And now, Russia — starved by war-related Western sanctions for technology like guidance systems for missiles and drones — is urgently seeking matériel.

“Military-technical cooperation between the two countries is permanently on the agenda,” Mr. Peskov told reporters on Wednesday, according to the Interfax news agency.

In Ukraine, officials in the southern city of Mykolaiv announced a drastic move on Friday: The area would be blocked off and placed under a strict curfew over the weekend as law enforcement agencies search for enemy collaborators.

The decision comes amid a significant escalation in Russia’s shelling of the city, which has had only about two dozen violence-free days since the war began on Feb. 24, officials said.

In recent weeks, officials have issued increasingly urgent warnings about the presence of subversive forces in the city, including those responsible for directing enemy fire at military targets. ‌

Vitaliy Kim, the military governor of the Mykolaiv region, urged residents to stock up on food and water and to cooperate with any law enforcement officials they might encounter over the weekend. Public transportation will also be shut down.

Mr. Kim did not specify how law enforcement agencies planned to go about finding enemy collaborators, but in recent weeks, he has offered cash rewards of $100 out of his own pocket to citizens who turn in suspected collaborators.

“Honest people have nothing to worry about,” Mr. Kim said. “We will be working on collaborators.”

Edward Wong reported from Phnom Penh, Cambodia, Neil MacFarquhar from Istanbul and Natalie Kitroeff from Mexico City.

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