Addressing supporters today, President Recep Tayyip Erdogan again defended Turkey's action and criticised Russia for its action in Syria before expressing his regrets.
Erdogan said: "We wish it hadn't happened, but it happened. I hope something like this doesn't happen again."
He says both sides should approach the issue in a more positive way. He says a meeting in Paris would be an opportunity to overcome tensions, and he renewed a call for a meeting with President Vladimir Putin in the sidelines of a Climate conference in Paris next week.
Turkey's Foreign Ministry today said it was issuing the warning because Turkish travellers were facing "problems" in Russia.
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It said Turks should delay travel plans until "the situation becomes clear."
Turkey's downing of the Russian military jet Tuesday, the first time in half a century that a NATO member shot down a Russian plane, has drawn a harsh response from Moscow.
Russia has since restricted tourist travel, left Turkish trucks stranded at the border, confiscated large quantities of Turkish food imports and started preparing a raft of broader economic sanctions.