Just two months in the past, many within the West thought President Recep Tayyip Erdogan of Turkey might be shifting away from what they thought of his overly shut relationship with President Vladimir V. Putin of Russia.

Mr. Erdogan had a warm meeting with President Biden. Turkey allowed a bunch of celebrated Ukrainian commanders, being held within the nation as a part of a prisoner change deal, to return to the battlefield, angering Russia. And Mr. Erdogan dropped his resistance to permitting Sweden to hitch NATO, strengthening the army alliance’s efforts to isolate Russia.

But there was no sign of a serious change in Mr. Erdogan’s balancing act between Russia and the West on Monday, when he and Mr. Putin stood aspect by aspect within the Russian resort metropolis of Sochi and spoke of additional increasing their nations’ partnership. They would enhance commerce and work collectively on power points, they mentioned, regardless of efforts by Mr. Erdogan’s NATO allies to cripple Russia’s financial system and restrict its entry to international power markets.

They additionally mentioned a extra urgent geopolitical matter — the resumption of an settlement to permit the export of Ukrainian grain by means of the Black Sea — though they introduced no concrete progress.

The leaders’ joint look made clear that their relationship endures and can possible proceed to develop, largely as a result of each side have extra to achieve from the partnership than they stand to lose, analysts mentioned.

As Russia finds itself ostracized from the West, Turkey has served as a significant channel, declining to hitch Western sanctions and persevering with to ship a lot wanted items to Russia. For Turkey, struggling with an economic crisis, Russia has proved a fertile marketplace for Turkish exports and has bolstered the Turkish authorities’s funds with delayed fuel funds and deposits in Turkey’s central financial institution.

“As far as Erdogan is concerned, he is, in my opinion, living in the best of both worlds,” mentioned Ahmet Kasim Han, a professor of worldwide relations at Beykoz University in Istanbul.

The Turkish chief has managed to take steps to please his NATO allies, like agreeing to confess Sweden to NATO and assembly with Mr. Biden, with out jeopardizing the various perks of his relationship with Mr. Putin.

Mr. Putin additionally advantages from his open channel with the chief of a NATO nation, Mr. Han mentioned, as a result of it provides him an oblique approach to talk his views to the remainder of the alliance, generally to the frustration of different members.

“If I were in the Kremlin, I would prefer a member of the alliance that sometimes hinders and delays issues that are of tactical importance to the members,” Mr. Han mentioned. “It is nice to have a nuisance like that among your rivals.”

Since Russia invaded Ukraine 18 months in the past, deciphering the connection between Mr. Putin and Mr. Erdogan has been an evolving puzzle for Western policymakers as they navigate the complicated diplomacy surrounding the warfare.

For the West, Mr. Putin is the battle’s villain, and the United States and different NATO members have sought to hobble his warfare machine with sanctions.

Mr. Erdogan staked out a extra complicated place, condemning Russia’s invasion and providing assist to Ukraine whereas increasing his nation’s financial ties with Russia and referring to Mr. Putin as “my friend.”

That method gave Mr. Erdogan a novel diplomatic function, permitting Turkey to assist dealer prisoner exchanges and the grain deal, which he and others have credited with facilitating meals deliveries to poor nations. But his refusal to shun Mr. Putin pissed off NATO allies and led some policymakers to privately query which aspect he was on.

This summer time appeared to supply indications that Mr. Erdogan needed hotter ties together with his NATO allies. During his assembly with Mr. Biden, Mr. Erdogan spoke of “a new process” with the United States. Mr. Erdogan welcomed President Volodymyr Zelensky of Ukraine to Turkey and mentioned that Ukraine “deserves NATO membership with no doubt,” a place that’s anathema to Russia.

But on Monday, it was clear how entwined Russia and Turkey have change into.

Mr. Putin famous how a lot commerce between Russia and Turkey had elevated in recent times. He talked about Turkey’s standing as a go-to vacation spot for Russian vacationers who now wrestle to journey elsewhere in Europe. About 5 million Russians visited Turkey final yr, Mr. Putin mentioned.

The two nations more and more cooperate on power points, and plan to take action extra sooner or later. Last winter, Moscow allowed Mr. Erdogan to delay funds for Russian fuel and permitted the Turkish authorities to make some funds in forex apart from {dollars}, easing stress on Turkey’s reserves.

For his half, Mr. Erdogan spoke proudly of a nuclear energy plant that Russia is constructing close to the Mediterranean coast in Turkey and expressed curiosity in a second one.

Alexander Gabuev, director of the Carnegie Russia Eurasia Center, mentioned the leaders additionally possible mentioned different points.

Both nations’ delegations included their central financial institution chiefs, suggesting talks about conducting extra commerce of their nationwide currencies, Mr. Gabuev mentioned. He additionally famous the attendance of Dmitri Shugayev, director of the Russian Federal Service for Military-Technical Cooperation, which means that army issues have been additionally possible mentioned.

“There is the underwater part of the iceberg, which we don’t know,” Mr. Gabuev mentioned.

Despite their discuss of elevated cooperation, the 2 leaders failed to revive the Black Sea grain deal, which had been brokered by Turkey and the United Nations final yr. Russia withdrew in July, saying that it had not obtained the advantages anticipated from the association.

Turkey and Russia have beforehand mentioned establishing a fuel hub in Turkey. The thought appeals to Mr. Erdogan as a approach to enhance Turkey’s weak place in international power markets, and it may enable Russia to promote its fuel to nations that may not purchase it straight.

Mr. Putin mentioned on Monday that the Russian state power big Gazprom had given a “road map” for the challenge to its Turkish counterpart, BOTAS.

Energy specialists, nonetheless, have questioned the viability of Mr. Putin’s proposal, saying it appeared unlikely that the European Union would approve new Russian fuel conduits or search to extend provides to Europe.

Europe has put considerable effort into lowering its reliance on Russian fuel imports and discovering different sources like liquefied pure fuel shipments from the United States, Qatar and elsewhere.

Ben Hubbard reported from Istanbul, and Paul Sonne from Berlin. Safak Timur contributed reporting from Istanbul, Stanley Reed from London and Marc Santora from Odesa, Ukraine.