Police detain at least 18 people, including a university head, over alleged coup plot.
Turkish media reported Babacan saying on his return to Ankara, the Turkish capital, that his country’s leaders wanted an “all-encompassing” solution and “full normalisation” of ties.
“We want a solution based on a wide perspective,” he said.
Turkey hopes that a deal with Armenia could aid their chances of joining the EU, but there remains differences between the two nations over the first world war killing of up to 1.5 million Armenians under Ottoman rule.
The incident is regularly cited as the first genocide of the 20th century, but Turkey denies that there was any systematic campaign to kill Armenians.
There is also discord over the Nagorno-Karabakh region, which Armenia gained from Azerbaijan after a six-year conflict at the end of the Soviet Union’s rule of both nations.
Turkey closed its border with Armenia in 1993 in support of Azerbaijian.
Ankara wants the talks with Armenia to run in parallel with negotiations between Armenia and Azerbaijan over the future of the region.
Azerbaijan has said that any deal between Ankara and Yerevan could only follow concessions from Armenia on the Nagorno-Karabakh issue.
The EU and US have both urged Armenia and Turkey to resolve their disputes and re-open their borders.
Hugh Pope, a senior analyst with the International Crisis Group, told Al Jazeera from Istanbul: “It is the best chance we have seen for a long time. It is a package deal. As far as we know they are gong to establish diplomatic relations, open that border and also have a commission to discuss the history of everything.
“And I think this comes after the two sides are really changing. On the one side we have a new government in Armenia over the past year. They are seeking some international legitimacy after the problems they had at the beginning.
“They are also seeking more work [and] the economy will be helped on both sides by opening the border.
“And also the weakness of Armenia. Its isolation was demonstrated quite graphically with the fighting in the Caucuses last year.
“And on the Turkish side we have a government that has for several years now been trying to improve relations with all its neighbours and it has proved that in Iraq and by opening up to Cyprus.
“There is a very strong tendency in Turkey especially in the intellectual elite to reassess the past and deal with what happened to the Armenians in a much more reasonable and open minded way.”