Exxon Mobil and the Russian oil firm Rosneft agreed to a deal Tuesday to begin joint operations on Russia’s Arctic Sea shelf and in the deep waters of the Black Sea, far to the south.

In return, Rosneft will get a chance to take part in Exxon’s operations in the Gulf of Mexico and Texas. The two companies said they also will pursue joint ventures in third countries.

Exxon agreed to invest $3.2 billion in opening oil and gas production in the Kara Sea, which is an arm of the Arctic Ocean tucked south of an island chain called Novaya Zemlya. Ice had made the Kara Sea too inhospitable for drilling operations in the past, but the recent advent of higher arctic temperatures makes it more attractive to oil companies.

Rosneft has calculated reserves in the Kara Sea’s East-Prinovozemelsky field at 35.8 billion barrels of oil and 10.3 trillion cubic meters of natural gas. It says the Tuapse field contains 2.2 billion to 7.2 billion barrels.

Russia’s economy depends heavily on petroleum exports, yet many of its oil fields in West Siberia are in decline. As such, the country is eager to tap into the vast unconventional oil resources of the Arctic. Yet the difficult environment means that Russian companies still rely on the expertise of Western producers such as Exxon, which has experience drilling in arctic regions of Canada.

Analysts note that the deal, while relatively small for Exxon in the near term, could be a boon over time. “With the potential that those Russian fields hold, this is certainly a win for Exxon and opens them up for a lot of potential oil growth in the future,” said Allen Good, an energy analyst at Morningstar.

An arctic exploration proposal between Rosneft and BP collapsed in May after BP failed to reach an agreement with its partners in its Russian venture. Analysts say the unexpected collapse of the BP deal, which had the blessing of Prime Minister Vladi­mir Putin, made the Exxon agreement all the more critical.

“That earlier strikeout was an embarrassment for Russia,” said Fadel Gheit, an oil analyst at Oppenheimer. “If this deal had fallen through, it would be hard to find further foreign takers.”

Putin was at the signing Tuesday, in the Black Sea resort of Sochi. According to Russian news services, he said the total value of the projects could be $200 billion to $300 billion, or even as much as $500 billion.

The deal also signals a thaw in U.S-Russian relations. Cliff Kupchan, director of the Eurasia Group, noted that just three years ago, U.S. energy firms were shut out of deals in Russia. “Since then,” he said, “we’ve had a reset in the relationship under President Obama, from cooperation on Iran to the START treaty, and we’re seeing that improved relationship seeping into energy.”

Exxon will take a 33 percent stake in the arctic and Black Sea projects. The details of Rosneft’s reciprocal participation in the Gulf of Mexico and Texas were not spelled out Tuesday.

The Black Sea exploration will take place in the Tuapse License Block, where the water is more than a mile deep. A preliminary agreement on that venture was reached in February.

The two companies also agreed to open a jointly staffed an Arctic Research and Design Center for Offshore Developments in St. Petersburg, Putin’s home town.

Rosneft became Russia’s largest oil company after it acquired assets of Yukos, which was broken up when Russian authorities decided to imprison its chief, Mikhail Khodorkovsky, in 2005. The Russian government holds a majority stake in the firm.

Plumer reported from Washington.