Russia has suffered heavy losses in Chechnya
The Russian authorities have welcomed Turkey's request for further information on Movladi Udugov, who Moscow labels the "main ideologist" of the Chechen rebels.
It is widely believed in Russia that Mr Udogov regularly visits Turkey and the Gulf States.
Delays in obtaining a response from Turkey about his possible extradition have caused tension between Moscow and Ankara.
The Chechen rebels have built up an extensive international network supplying money, weaponry and propaganda support.
Extradition hurdles
Russia will face serious difficulties in persuading foreign governments to help, but the hunt for Mr Udugov is one of the priorities in Moscow's campaign to crush what remains of the Chechen insurgency.
He stands accused since March 2000 of one of the most serious crimes in Russia's criminal code - "armed rebellion".
What makes him a particularly important target for Moscow is his role in sporadically contacting the international media with reports contradicting Moscow's official line.
And his ability to elude capture and justice humiliates Russia's military and security chiefs.
Foreign support
The Chechen rebel leaders have extended their presence and influence in a number of countries.
This lies at the heart of Moscow's argument that the rebellion is about international terrorism, not a neo-colonial war to retain territory historically incorporated into the Russian state by conquest.
There is a network of sorts. Its efficiency is questionable, but support for the rebellion does rely on a number of international factors.
There is convincing evidence that money and arms have been supplied in ample amounts by a number of Islamic states.
In particular, Afghanistan's former Taleban regime supplied heavy weaponry to rebel fighters and Moscow claims a significant number of rebels underwent training at al-Qaeda camps in Afghanistan.
Saudi Arabia is suspected of being another major source, supplying the foreign Wahhabi fighters led by the warlord Khattab.
Chechen rebel spokesmen have operated out of France and Belgium.
Anti-Russian propaganda praising the Chechen 'Jihad' is carried on dozens of influential foreign-registered websites and Moscow accuses a number of Western governments of ignoring Islamic organisations' fund-raising activities on behalf of the rebels.
But diplomatic protocols and high-level negotiations may not be enough to guarantee Mr Udugov's extradition.
Firstly, his exact whereabouts are unknown. Turkey is home to the largest Chechen diaspora outside the republic itself and the extradition would be deeply unpopular.
Secondly, Moscow's dismal human rights record in Chechnya does not predispose foreign governments towards helping Moscow, especially those governments, like Turkey, which aspire to membership of the European Union.
Thirdly, if Mr Udugov has taken refuge elsewhere in the Middle East, Islamic unity is likely to be a significant factor in hindering any extradition.
There are other countries in the region with Chechen communities. Jordan is home to the second largest diaspora, the descendants of Chechen families who fled Russian oppression in the South Caucasus in the 19th century.
In these states, there is likely to be no official sympathy for extraditing people Moscow accuses of terrorism.