Before such a group could be established, the Vatican would have to approve it, said Dang Tai Tinh, a member of Vietnam's Committee on Religious Affairs.
The Vatican delegation, led by Monsignor Pietro Parolin, met with government and church officials in Hanoi and four provinces. They returned to Rome on Sunday, the AP says.
It was the 15th time Vatican representatives have made an annual visit to Vietnam, but this year's meetings drew heightened attention because of the prospect the two sides might establish diplomatic relations.
They announced that possibility in January after Pope Benedict XVI received Prime Minister Nguyen Tan Dung, the highest-level Vietnamese official to visit the Vatican.
For decades there have been tensions between the Vietnamese government and the Roman Catholic Church, particularly over Hanoi's insistence on having the final say in most church appointments.
But after the Pope's meeting with Dung, the Vatican said there had been "concrete progress" for religious freedom for the church in Vietnam.
Vietnam's 6 million Catholics are Southeast Asia's second-largest Catholic population after the Philippines.
Russian Finance Minister Anton Siluanov announced a possible move that Russia can take in response to new US sanctions
Not that long ago, American soldiers would train their skills to counter insurgent and partisan military organizations. These days, they are trained to show resistance to the regular army of a potential adversary
The Central Bank of Turkey announced measures to protect the financial market of Turkey against the background of the collapse of the Turkish lira and conflict of interests with the United States of America