A French police spokesman summed it up: "The only certainty for the moment is that this is a triple homicide."

His remarks will, of course, do little to stem speculation over who carried out the execution-style killings of three female Kurdish activists whose bodies were found in a Paris political office yesterday morning.

That one of the women, Sakine Cansiz, was a co-founder of the Kurdistan Workers Party (PKK) – an organisation deemed a terrorist group by Turkey, the United States and the European Union – will only further fuel the range of conspiracy theories emerging over the motive for the assassinations.

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A triple homicide it certainly was, but there is another certainty about yesterday's killing – the simple fact they could not have come at a more crucial moment.

It can surely be no coincidence the gunning down of Ms Cansiz and her colleagues happened not only just as the Turkish government opened talks with Abdullah Ocalan, the PKK leader serving a life sentence on the prison island of Imrali, near Istanbul, but at a time when the more militaristic factions within the PKK – emboldened by their Kurdish allies' successes in Syria – have been gaining an upper hand within the organisation.

Right now, the turmoil inside Syria, and elsewhere across the region where the Kurdish people find themselves scattered, has presented the PKK with a pivotal political opportunity.

In the eyes of many Kurds, their moment has come and they must seize the opportunity by whatever means they can.

Which takes us back to the two main theories about the motive for yesterday's murder of the three Kurdish activists.

What both have in common is that the triple killings are linked to an attempt to disrupt the peace talks between Turkey and Ocalan. Indeed, across Turkey, news of the killings almost instantly overtook latest reports of the negotiations – the first confirmed state-PKK talks since mid-2011.

While nothing certain is known about the specific content of the talks, the fact Turkish Prime Minister Tayyip Erdogan took clear responsibility for the meetings has created hope for a breakthrough. This, after all, is a conflict that has seen some 40,000 people killed since the 1980s, most of them Kurds angry at a Turkish state they claim has regularly rode roughshod over their human rights.

If reports in the Turkish news-paper Radikal are accurate, Ocalan had drawn up a four-stage plan to bring about peace.

It includes the withdrawal of Kurdish fighters from Turkish territory, who would then engage in disarmament talks before laying down their weapons.

The plan would also see the Turkish government releasing from custody thousands of people accused of links to the PKK and there would be constitutional reforms to remove obstacles to Kurdish language education, strengthening local administrations and creating an ethnically neutral definition of citizenship.

Not everyone, however, seems to have bought into these ideas, with some elements both within the Turkish state and the PKK itself bitterly opposed.

Intelligence analysts point to a what they say is a so-called "deep state" or "dark forces"– a powerful nationalistic establishment within Turkey who want to see the peace initiative fail.

That was the suspicion – albeit unsubstantiated – of the many Kurdish activists who gathered yesterday to demonstrate outside the information centre of the Kurdish institute in Paris, where the bodies of Ms Cansiz and her colleagues were found.

Other analysts, however, point not to dark forces within the Turkish establishment but an internal feud within the PKK as the likely motive behind the killings.

Some sources emphasise murdered Ms Cansiz was known for her opposition to the alleged head of the PKK's armed-wing, a Syrian citizen called Ferman Hussein.

Huseyin Celik, deputy chairman of Turkey's AK Party, was one of many who made the point that internal feuds within the PKK have blown up in the past whenever there were signs of progress towards peace.

"Whenever in Turkey we reach the stage of saying 'friend, give up this business, let the weapons be silent', whenever a determination emerges on this, such incidents happen," was how Mr Celik summed it up.

Perhaps one of the biggest problems with the ongoing Ocalan-government talks is that the PKK leader is stuck in a jail near Istanbul far removed from the PKK's military leadership in the field who see the current instability gripping the region as an opportunity not to talk but to pile on the pressure through armed struggle.

The organisation's internal politics is further complicated by the fact there is not one but many PKKs – given that the movement exists in Syria, Iran and Iraq, all of whose governments have in the past used the Kurdish card for political leverage over Turkey.

Despite the ongoing talks with Ocalan, Ankara's battlefield struggle with the PKK has recently had its worst casualty rates since the 1990s. As many as 870 people been have been killed since the PKK resumed its attacks and Turkish security forces revived their counter-terrorism operations in mid-2011.

Few observers doubt the Kurdish question has taken on a fresh urgency with the rise of Kurdish groups across the region.

Many Turks also fear Syrian President Bashar al Assad could encourage Kurds to feed militancy in Turkey. That growing regional Kurdish threat, not to mention a slowing Turkish economy, will undoubtedly factor into the domestic political skirmishing ahead of the country's presidential election in 2014.

For some time now, Mr Erdogan has been bracing himself for that political showdown by aligning ever more firmly with right wing and nationalist voters who have little truck with the Kurdish cause, despite the fact Kurds make up more than 20% of Turkey's 75 million people.

Whoever was behind yesterday's killings in Paris, there is little doubt timing was uppermost in their minds.

That the deaths of the activists will make the current peace negotiations even more difficult is a given. They may even scupper them entirely.