President Nguyen Minh Triet met with Benedict for 40 minutes - twice as long as was scheduled and the first time that the head of state of Vietnam has met with the pope since the communists took power in 1954.
On the eve of the trip, Triet had told an Italian newspaper that his government is working to open diplomatic relations with the Vatican. Vietnam's 6 million Roman Catholics is one of the largest Catholic communities in Asia.
"The Holy See expressed its pleasure at the visit, a significant stage in the progress of bilateral relations, and expressed the hope that outstanding questions may be resolved as soon as possible," the Vatican statement said.
There have been tensions between Catholics and the Hanoi government over church property seized by the Communists. The government also closely monitors religious groups and insists on approving most church appointments.
The Vatican said "the cordial discussions provided an opportunity to touch upon certain themes concerning cooperation between church and state," but the statement did not elaborate.
When the meeting was opened to reporters, both men seemed pleased with the discussions.
In his interview published Tuesday in Corriere della Sera, Triet described himself as an atheist but said he goes to churches and pagodas because "I recognize the cultural value" of religious feasts.
Church officials have spoken about the possibility of a papal visit to Vietnam, but the Vatican statement did not mention such a trip.