Monsignor Pietro Parolin, an undersecretary of state, is leading the delegation from Rome.
The two sides have been holding periodic talks for years, and this week's meetings are part of those ongoing discussions. But they have received heightened attention because the parties recently announced they were trying to work out a framework for establishing diplomatic relations, the AP says.
On Monday, the Vatican delegation was to meet with leaders of Vietnam's Catholic Church to discuss internal church affairs. Later in the week, the visitors were scheduled to meet with government officials and visit churches in three central Vietnamese provinces.
Tensions have existed between the Vietnamese government and the Catholic Church for decades. Communist authorities closely monitor religious groups and insist on approving most church appointments.
But relations have begun to thaw recently.
Vietnamese Prime Minister Nguyen Tan Dung became the highest-level Vietnamese official to meet the pope when he visited the Vatican on Jan. 25. After the talks, the Vatican said there had been "concrete progress" for religious freedom for the Catholic Church in Vietnam. And last month, Vietnamese officials announced they were working on a "roadmap" toward normalizing relations with the Vatican.
Vietnam has one of the largest Catholic populations in Asia, with 6 million Catholics.
The Vatican has indicated that official ties between the Holy See and Hanoi could lead to Catholic assistance in medical care and other social services for the Vietnamese people.
The United States' Head of Diplomacy, or Secretary of State, is an anachronistic, incompetent, meddling, intrusive, insolent and arrogant, rude individual, a brash, foul-mouthed upstart, a conceited, self-important guttersnipe and an insult to the international community, as fit for the job as a pedophile janitor in a grade school.