Ankara and Yerevan have no diplomatic ties and the border between the two countries is shut, with the relationship shadowed by the mass killings of Ottoman Armenians in World War I which Armenia considers a genocide.
Pashinyan swept to power this week after veteran leader Serzh Sarkisian renounced his plan to be prime minister following 10 years as president in the face of bitter protests.
The new premier later said that "we are keeping with our position and we are ready to establish relations (with Turkey) without conditions."
"Let's see first," Turkish Prime Minister Binali Yildirim told reporters in Ankara on Friday.
"If Armenia gives up its hostile attitude which it has had for several years, its attitude towards Turkey's territorial integrity and borders, if it is giving up all its wrong attitudes... and it wants to open a new page, we will give the response looking at the details relating to this."
"We are going to increase friends, we are going to reduce enemies," Yildirim added.
'Committed to genocide recognition'
Turkey vehemently rejects that the massacres, imprisonment and forced deportation of Armenians from 1915 -- which Yerevan says left 1.5 million dead -- constituted a genocide.
The issue has so far stymied efforts to forge relations, with tensions only increasing around the 100th anniversary of what Turkey terms the "1915 events" in 2015.
Sarkisian in March formally ditched 2009 agreements that would have normalised relations with Turkey which were thrashed out under the aegis of Russia, France and the US but never ratified by either parliament.
Even if Turkey and Armenia found a way to establish ties, Ankara would have to placate its ally Azerbaijan which remains wary of any warming between Turks and Armenians.
Baku has repeatedly threatened to retake by force the Azerbaijani region of Nagorny Karabakh which is controlled by Armenian separatists after the war in the early 1990s.
Pashinyan said earlier this week it was Turkey who was imposing "illogical" conditions.
"It is illogical to make conditions referring to a third country (Azerbaijan) when you want to establish relations," he said in Stepanakert, the main town of Nagorny Karabakh which is not recognised by any state including Armenia.
He emphasised that Armenia "remains committed to international recognition of the Armenian genocide."
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