By Olesya Astakhova and Nick Tattersall

ISTANBUL (Reuters) - Turkey and Russia signed an agreement on Monday for the construction of a major undersea gas pipeline and vowed to seek common ground on the war in Syria, accelerating a normalization in ties nearly a year after Turkey shot down a Russian warplane.

Turkish President Tayyip Erdogan hosted Russia's Vladimir Putin at an Ottoman-era villa in Istanbul for talks which touched on energy deals, trade and tourism ties, defense and the conflict in Syria, where the two leaders back opposing sides.

"Today has been a full day with President Putin of discussing Russia-Turkish relations ... I have full confidence that the normalization of Turkish-Russian ties will continue at a fast pace," Erdogan told a joint news conference.

The warming relations between NATO member Turkey and Russia comes as both countries are dealing with troubled economies and strained ties with the West.

Putin said Moscow had decided to lift a ban on some food products from Turkey, imposed after the Turks shot down a Russian fighter jet near the Syrian border last November, and that both leaders had agreed to work toward the full-scale normalization of bilateral ties.

They signed a deal on the TurkStream undersea gas pipeline, which will allow Moscow to strengthen its position in the European gas market and cut energy supplies via Ukraine, the main route for Russian energy into Europe.

The plan for TurkStream emerged after Russia dropped plans to build the South Stream pipeline to Bulgaria due to opposition from the European Union, which is trying to reduce its dependence on Russian gas.

Erdogan also said plans for a Russian-built nuclear power plant in Turkey would be accelerated. Time lost on the Akkuyu project because of strained relations would be made up, he said.

In 2013, Russia's state nuclear corporation Rosatom won a $20 billion contract to build four reactors in what was to become Turkey's first nuclear plant, but construction was halted after the downing of the Russian jet.

DEEP DIVISIONS ON SYRIA

Putin received Erdogan in a Tsarist-era palace outside his home city of St Petersburg in August, when the two leaders, both powerful figures ill-disposed to dissent, announced plans for an acceleration in trade and energy ties.

But progress on Syria, over which they remain deeply divided, has been more problematic. Erdogan described the topic as "very sensitive", but said he had discussed Turkey's military operations in Syria with Putin on Monday.

Both men said they had agreed on the importance of delivering aid to the city of Aleppo, whose opposition-held eastern sector has been encircled by Russian-backed Syrian forces for all but a short period since July.

"We have a common position that everything must be done to deliver humanitarian aid to Aleppo. The only issue is ... ensuring the safety of aid delivery," Putin said, adding he had agreed with Erdogan to intensify military contacts.

Russia has backed Syrian President Bashar al-Assad with a year-long air campaign against the rebels fighting him. Turkey backs the rebels and wants to see Assad out of power.

On Saturday, Russia vetoed a French-drafted U.N. Security Council resolution that would have demanded an end to air strikes and military flights over Aleppo. A rival Russian draft text failed to get a minimum nine votes in favor.

Erdogan said there would be further talks with Russia over the conflict in Syria. But there was little sign of any concrete progress toward reconciling their differences.

"We discussed ... how we can cooperate on this matter, especially on humanitarian aid to Aleppo, what strategy can we implement so people in Aleppo can find peace," Erdogan said.

"We will come together with our foreign ministries and top military leaders and intelligence officers."

(Writing by Nick Tattersall; Editing by Anna Willard)