Recep Tayyip Erdogan said he wished the incident had not happened and hoped it would not happen again.
The Turkish president has so far refused to apologize to Russia, accusing Moscow of “playing with fire” in its Syria operations.
His remarks came as Turkey warned its citizens against non-essential travel to Russia.
The Foreign Ministry said visits should be avoided “until the situation becomes clear”, citing problems such as anti-Turkish demonstrations outside Turkey’s embassy in Moscow.
On November 27, Russia suspended its visa-free arrangement with Turkey and is planning to introduce a wide range of economic sanctions.
Recep Tayyip Erdogan has asked for a meeting with Russian President Vladimir Putin, but Vladimir Putin wants an apology from Turkey before he will agree to talks.
The Turkish president again defended the incident and criticized Russia’s operations in Syria in support of President Bashar al-Assad, whom Ankara opposes.
He renewed his call for a meeting with Vladimir Putin on the sidelines of the Paris Climate talks next week, saying that both sides should approach the issue more positively.
“We wish it hadn’t happened, but it happened,” Recep Tayyip Erdogan said, quoted by the Associated Press.
“I hope something like this doesn’t happen again.”
Russia has sent troops and aircraft to Syria to back up the Syrian government of Bashar al-Assad in the civil war.
Turkey, which is a member of NATO and of a US-led coalition in the region, insists Bashar al-Assad must step down before any political solution to the Syrian conflict is found.
Both countries say they are trying to rid the region of ISIS, which claimed the recent attacks on Paris, Ankara and also on a Russian airliner.
On November 27, Russia said it had strengthened its anti-aircraft defenses by moving a cruiser towards the coast and deploying new missiles at its main base.
The Moskva cruiser’s long-range air defense system will provide cover for Russian aircraft, as will the S-400 missiles which arrived on November 26.
Turkey says the Russian combat jet had intruded into its airspace and ignored warnings to leave.
Moscow maintains that the downed SU-24 fighter jet was downed by a missile fired from a Turkish jet inside Syria.
Vladimir Putin has also firmly rejected any suggestion Turkey did not recognize the plane as Russian. He said it was easily identifiable and its co-ordinates had been passed on to Turkey’s ally, the US.
On November 26, Russia on said it was drafting a wide-ranging list of economic sanctions against Turkey that would hit food imports and joint investment projects among other things.
Turkey and Russia have important economic links. Russia is Turkey’s second-largest trading partner, while more than three million Russian tourists visited Turkey in 2014.
Recep Tayyip Erdogan’s latest statement on the downing of the plane came in an address to supporters in Balikesir, western Turkey, following the murder of a senior Kurdish lawyer, Tahir Elci, in the south-eastern city of Diyarbakir on November 28.
Tahir Elci was shot dead by an unknown gunman as he called for an end to violence between Turkey and the Kurdish rebel PKK group, which resumed in July.
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