MOSCOW — Amid increasingly tense relations with the United States over Syria, President Vladimir V. Putin of Russia took advantage of a routine meeting in Istanbul on Monday to advance the Kremlin’s reconciliation with Turkey, including an agreement to revive a suspended natural-gas pipeline project.

The new pipeline, known as the Turkish Stream, would run under the Black Sea to Turkey and then the Greek border, allowing Russian gas to reach Western markets without using Russia’s existing export pipelines through Eastern Europe.

The pipeline would make it much easier for Russia to cut off gas supplies to neighboring countries like Ukraine without disrupting sales to countries farther west like Italy or Austria. Russia has been trying for years to establish such an export route.

Mr. Putin’s appearance at an international energy conference was his first visit to Turkey since a crisis in relations between the countries after Turkey’s downing of a Russian fighter jet along the border with Syria in November 2015, in which a Russian pilot was killed. President Recep Tayyip Erdogan of Turkey, nominally an ally of the United States in Syria, patched things up with a letter of apology and a trip to St. Petersburg in August.