Can Russia and Turkey heal rift?

The Russian warplane came down in a mountainous area of northern Syria

Since the downing of the Russian jet by Turkish forces in November, relations between Turkey and Russia have been in a pattern of controlled tension. The war of words has been interesting to watch.

On Tuesday, came another round. Turkey accused Russia of an attack on a hospital in Idlib - something Moscow denied. In retaliation, Moscow called on Ankara to withdraw troops from northern Iraq immediately.

Later in the day though, a departure from the months-long, tough rhetoric came surprisingly from Turkey's President Recep Tayyip Erdogan.

Mr Erdogan said he was concerned at how relations had been sacrificed over what he called "a pilot error", referring to the downing of the jet which Turkey claims had violated its air space.

He also said he wanted to improve ties with Russia but that he did not understand what kind of "first step" Moscow was expecting.

Russia's President Vladimir Putin was clear about that: Moscow expects a formal and public apology from Turkey and also compensation for the jet incident.

Not something that Ankara seems likely to do.

"Turkey wants to take a step, but does not want to give the impression that this would indeed be a step back," says diplomacy expert Semih Idiz.

"There is no international pressure on Turkey to apologise. I don't think it is going to happen."

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Experts believe Mr Erdogan regrets his reaction to the Russia jet incident

The downing of the Russian jet changed Turkey's involvement in the Syrian conflict considerably.

As Russia maintained a de facto no-fly zone in northern Syria by the Turkish border, Turkey lost its ability to give air support to Syrian rebels or protect its borders from Islamic State (IS) militants' shelling.

"If Erdogan could rewind one foreign policy move, that would be the downing of the Russian plane. He regrets it so much," says Soner Cagaptay from US-based think tank Washington Institute.

"But given Mr Erdogan's personality, I think an apology is highly unlikely. It would be the first time Erdogan would have admitted to a foreign policy failure."

Many also think a public apology could be seen as demeaning by the nationalists whose support Mr Erdogan needs in order to be able to change the system in Turkey from parliamentary to presidential, giving him significantly greater executive powers.

"Neither Mr Erdogan nor the ruling party can take that risk and pay that political price. No apology can come before the whole debate on regime change is over," says academic Ahmet Kasim Han.

Proxy war in prospect?

Although the tension between the two countries could be unsustainable in the long run, no one actually thinks that this could evolve into an all-out war. However, many expect a proxy escalation.

On 13 May, a Turkish Cobra helicopter was shot down by the Kurdish militia group PKK over south-eastern Turkey, killing two pilots. A Russian-made man-portable air defence system (Manpads) was used in the attack.

• In detail: Russia and Turkey tit-for-tat

Mr Putin expects a formal and public apology from Turkey

On Monday, President Erdogan accused Russia of supplying weapons to the PKK. Moscow asked the Turkish government to provide evidence.

It is not clear whether Russia handed weaponry to the PKK or whether the PKK bought the missile on the black market in Syria or Iraq.

But because of the historical ties between the PKK and Moscow, the general assumption in Turkey is that the PKK is being used by Russia as a proxy in the recent escalation.

"Russia might provide weapons to the PKK, they are already giving weapons to the PYD (Kurdish Democratic Union Party), they have promised recognition to Rojava (Kurdish entity in northern Syria), Russians are escalating against Turkey through the use of proxy issues. I think that's going to be the long-term vision moving forward," says Soner Cagaptay.

This, however, presents many risks for Turkey. A Russian MP recently warned that Moscow would arm the PKK with Manpads if Washington and its allies allowed such weapons to reach Syrian opposition groups. Two weeks after this, the Turkish helicopter was shot down.

The PKK having the ability to use Manpads against Turkish forces poses a serious threat, says defence analyst Can Kasapoglu.

"We do not know how many Manpads the PKK currently has. That would be classified information of the Turkish intelligence. So we can't speculate on how big a threat this is."