Mr Gul's decision to accept an invitation from Armenia's president, Serzh Sarkisian, has raised expectations that Turkey may establish diplomatic ties and open the border it closed during the 1990s fighting between Armenia and Azerbaijan over Nagorno-Karabakh.
Relations between the two were disrupted 16 years ago over Armenia's occupation of Nagorno-Karabakh, an enclave in Azerbaijan.
It is also wary of Russia's show of wanting to help Armenia and Azerbaijan make peace over Nagorno-Karabakh.
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For Mr Kocharian is a former leader of the disputed (but Armenian-controlled) territory of Nagorno-Karabakh, which was conquered by Armenia in 1993 but is still recognised internationally as part of Azerbaijan.
Mr Erdogan declared that friendship with Armenia was no longer possible unless it withdrew from Nagorno-Karabakh.
The Azeris reckon with some evidence that Russia helped Armenia win the war against them for the disputed Nagorno-Karabakh territory.
Azerbaijan fought a war with neighbouring Armenia in the 1990s, in which it lost the Nagorno-Karabakh region, and the two sides may yet fight another.
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Indeed, absent Russian efforts to reduce tensions, Armenia and Azerbaijan would almost certainly have gone to war over Nagorno-Karabakh sometime over the past five or six years.
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Unlike chess-players, though, all the participants can win in this game, it is hoped, if they agree on a common aim: peace between Turkey and Armenia, which would help to thaw the frozen conflict between Armenia and Azerbaijan over the (mainly Armenian) territory of Nagorno-Karabakh.
These were sealed in 1993 after Armenia's short war with Azerbaijan over the mainly Armenian enclave of Nagorno-Karabakh.
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On 26th September President Ter-Petrosian told the Karabakh Armenians that their demand for independence or unification with Armenia was simply "unrealistic".
Even before the Georgian war, Turkey seemed to understand that isolating Armenia is not making it give up the parts of Azerbaijan that it occupies outside Nagorno-Karabakh.
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