While revenue from a new gas pipeline could be years away, such a project — whether with Russian or Western backing — would have obvious allure for Greece.

The Russian proposal is for a pipeline called Turkish Stream. It is intended to replace an earlier Russian initiative for a pipeline to Europe called South Stream, which Mr. Putin was forced to abandon late last year because of European Union rules that would have made the project unpalatable to Moscow by requiring Gazprom to share the pipeline with other suppliers. The South Stream pipeline, running under the Black Sea, would have brought gas into the European Union through Bulgaria.

Mr. Hochstein, the American official, said on Friday that the pipeline he was promoting — called the Southern Gas Corridor project — was farther along in construction. It would involve multiple companies, including the British energy giant BP, and countries including Georgia and Turkey, and it would bring together a series of pipeline projects stretching from Azerbaijan to Italy, through Greece.

When the route now known as the Southern Gas Corridor was first proposed more than a decade ago, it was called Nabucco and did not include Greece. Instead, its entry point to the European Union would have been Bulgaria. But Azerbaijan subsequently selected other routes for transporting its gas, including one that would run from the Turkish border through Greece and Albania into Italy. Work has begun in eastern Turkey on another portion of the pipeline.

Greece’s government, and its predecessor, have both agreed in principle to the Greek portion of the pipeline from Azerbaijan. But Athens and the Azerbaijanis have not yet been able to come to terms on the financial portion of a deal and other details. Mr. Hochstein on Friday was urging Greece to press ahead with the project.

“It is an excellent project for Greece as it will create a significant amount of jobs,” Mr. Hochstein said.

In a statement released on Friday, the United States Embassy in Athens said the portion of the pipeline crossing Greece would result in €1.5 billion in foreign investment in Greece, generate 10,000 jobs during construction, and provide many millions of euros in revenue each year for the next quarter-century.