But this slogan is being put to the test these days, following Turkey and Armenia's recent signing of protocols to restore diplomatic relations and open up their borders. That's something Azerbaijan is strongly opposed to, in the wake of the deal with Armenia that doesn't address a territorial dispute between Azberbaijan and Armenia.
The new tension between Ankara and Baku is raising concern that the Azeris – who sit on top of large reserves of oil and gas – might scuttle energy deals that involve Turkey, especially the Nabucco pipeline project, designed to ease Europe's dependence on Russian natural gas.
As Turkey tries to deal with one of its historic problems in order to improve relations with a neighbor, it appears other historic problems are creating new tension with another neighbor, with possible consequences for European energy security.
"If those countries which are genuinely interested in the Nabucco project influence Armenia so that it steps back from the occupied territories and both Azerbaijan and Turkey will be satisfied, then this will be remembered as only an episode in Turkey-Azerbaijan relations," says Ilgar Mammadov, a political analyst based in Baku.
"If not, then the relationship between Turkey and Azerbaijan will worsen, and projects like Nabucco will be undermined."
The protocols make no mention of Nagorno-Karabakh, a mountainous Azeri territory occupied by Armenian forces since 1994. Turkey first closed its border to Armenia in response to its occupation of the territory and Azeri officials have said Ankara's relations with Yerevan should not be restored until the frozen Nagorno-Karabakh issue is settled.
Baku feels betrayed
The reaction in Baku to the deal signed by Turkey and Armenia – which must still be ratified by the two countries' parliaments to take effect – has been particularly strong. Turkish flags have been taken down in the city and Azerbaijani President Ilham Aliyev, speaking at a nationally televised cabinet meeting on Oct. 16, suggested his country might stop selling Turkey natural gas at a discounted price.
"Azerbaijan is looking at the opening of the Turkey-Armenia border as a betrayal. We are looking at Turkey as our main partner in the region and [at] Armenia as our main enemy. The reaction is natural," says Vafa Guluzade, former foreign affairs advisor to the previous Azeri president, Haydar Aliyev.
Turkish officials have been making efforts to appease Baku, making it clear that they will not move forward on renewing ties with Armenia until the Nagorno-Karabakh issue is resolved.
"Nothing can change the fact that Turkey will always stand by Azerbaijan and Turkey's position on Azerbaijan's territorial integrity and its territories under occupation," Turkish Foreign Minister Ahmet Davutoglu said during a Thursday visit to the Azeri capital.
But Guluzade, the former Azeri foreign affairs adviser, says Baku is looking for stronger reassurances.
However, Huseyin Bagci, a professor of international relations at Ankara's Middle East Technical University, says that in the long run, the opening of the Turkey-Armenia border will actually facilitate the resolution of the Nagorno-Karabakh issue.
"Azerbaijan has to realize that discussion of the Nagorno-Karabakh issue can only happen if the Turkey-Armenia border opens," he says.
In the meantime, without a resolution to the conflict between Azerbaijan and Armenia, Ankara and Baku may find the "one nation-two states" slogan being further tested, Bagci says.
"It's a nationalist slogan, it's nice to hear, but it's never been the case," he says. "We have never been one nation."
What are Turkey and Armenia doing to get past decades of hostility? Read more here.