Russian President Vladimir Putin and his Turkish counterpart Recep Tayyip Erdogan looked to rebuild ties as they met on Tuesday for the first time since Ankara downed one of Moscow's warplanes in November.

Erdogan's visit to Putin's hometown of St. Petersburg is also his first foreign trip since the failed coup against him last month that sparked a purge of opponents and cast a shadow over Turkey's relations with the West.

"Your visit today, despite a very difficult situation regarding domestic politics, indicates that we all want to restart dialogue and restore relations between Russia and Turkey," Putin said after the two leaders shook hands.

Erdogan, who has said the trip represents a "new milestone", told Putin that ties had entered a "very different phase", and he thanked the Kremlin leader for his backing after the coup attempt.

The shooting down of a Russian fighter jet by a Turkish F-16 over the Syrian border last fall saw Putin slap economic sanctions on Turkey and launch a war of words with Erdogan.

But in late June, Putin surprisingly accepted a letter expressing regret over the incident from Erdogan as an apology and quickly rolled back a ban on the sale of tour packages to Turkey and signaled that Moscow would end measures against Turkish food imports and construction companies.

Putin was one of the first foreign leaders to phone Erdogan offering support after the coup attempt.