The talks in Germany mark the sixth encounter for the Armenian and Azeri president.
Patience 'running thin'
Prior to the meeting, Aliyev warned that his country’s military was ready to take back the mountainous territory by force.
"We have the full right to liberate our land by military means"
In comments broadcast on Saturday, he also warned Azeri patience was running out, a statement analysts say reflects rising tension over the prospect of Turkey opening its border with Armenia, which oil-producing Azerbaijan vehemently opposes.
"If that meeting ends without result, then our hopes in negotiations will be exhausted and then we are left with no other option. We have the full right to liberate our land by military means," Aliyev said.
But a bid by Turkey and Armenia to bury a century of hostility stemming from the mass killing of Armenians by Ottoman Turks has thrust the Caucasus conflict back into the diplomatic spotlight.
Natalia Leshchenko, an expert on the Caucasus region, told Al Jazeera: "This conflict has been frozen for almost two decades now so its unlikely it would erupt into war. Besides, the Azeri leader is aware of the fact that he would have to play against all the great powers of the world by trying to start a conflict."
She said: "This is almost being done for the benefit of the domestic audience to say that he will go ahead with these talks."
Ankara and Yerevan have signed accords to establish diplomatic ties and open their border, which Turkey closed in 1993 in solidarity with Azerbaijan during the war.
The deal carries huge significance for Turkey's diplomatic clout in the strategic Caucasus region, for its bid to join the European Union, and for landlocked Armenia's crippled economy.
But Azerbaijan has reacted angrily, fearing it will lose leverage over Armenia in the Nagorno-Karabakh conflict.
US, Russian and French mediators say they are making progress in intensified talks, but Western diplomats say neither side appears ready to commit to painful concessions.
The principles of a new deal would allow ethnic Armenian forces to give back most of seven Azeri districts surrounding Nagorno-Karabakh that they captured during the war.
If the deal is approved the territory would then be granted greater international legitimacy before a popular vote in the future to decide its final status.
Nagorno-Karabakh has been under control of Armenian troops and ethnic Armenian forces since a 1994 ceasefire deal that ended six years of war and killed at least 30,000 people.
The territory of 100,000 people wants recognition as an independent state, but 15 years of mediation have failed to produce a peace deal.
Instead, sporadic exchanges of fire continue to threaten war in a key oil and gas transit region to the West.