Turkish President Abdullah Gul visited Armenia in September
Armenia has urged Turkey to re-open the two countries' common border, which has been closed since 1993.
Speaking in Istanbul, Armenian Foreign Minister Edward Nalbandian said improving relations would boost regional peace and stability.
The two nations have waged a war of words over what Armenia says was the genocide of Armenians by Ottoman forces during World War I.
Turkey denies any genocide, saying the deaths were a part of the war.
"Relations should be improved without any preconditions," Mr Nalbandian told a news conference in Istanbul.
The handling of the killings is still extremely sensitive
"I think re-opening the border is also among Turkey's priorities; it is important for both countries' interests," the minister added.
The two countries have had no diplomatic ties since Armenia became independent after the collapse of the Soviet Union in 1991.
Their common border has remained closed since the war between Armenia and Turkey's ally, Azerbaijan, over the disputed territory of Nagorno-Karabakh.
Earlier this year, Turkish President Abdullah Gul made a landmark visit to Armenia - the first Turkish leader to do so.