Although tensions remains, the BBC's Nga Pham reports the visit has raised hopes of reconciliation between the two sides.
On 23 November, around 100,000 believers gathered in a small town near Hanoi to celebrate the 350th anniversary of Catholicism in Vietnam.
That evening, a message by Pope Benedict XVI was read before a sea of flickering candles and pious eyes.
The Pope wrote that the jubilee was " a time for reconciliation", as well as of building "a just and fair society… through genuine dialogue, mutual respect and healthy collaboration".
The message of "reconciliation and hope" was a fresh sign of efforts to bridge the divide between the communist country and Catholicism.
It came after a period that saw large protests erupting in Hanoi and elsewhere in Vietnam to reclaim Catholic lands and properties seized by the communist government when it came to power.
Whose land?
Land remains one of the thorniest issues in the relations between the Church and the state.
The Vietnamese government maintains that all land belongs to the state and refuses to discuss "historical claims" dating back to colonial times.
The government has rejected requests to return the Vatican Ambassador's residence in Hanoi, a church in Quang Binh, central Vietnam, and most recently a seminary in Dalat in the Central Highlands.
The protests over the properties were dealt with promptly and harshly.
In a fast-growing economy like Vietnam, land, apart from its religious significance, can also have great financial value. That reason alone is enough to ignite resentment between local communities and the Catholic church.
Booming belief
Official ties between the two sides were severed in 1959, when the Vatican's ambassador was removed from Hanoi.
Since then, the bilateral relationship has moved a long way, with dozens of talks held in the last two decades.
And although the authorities maintain control over religious activities, Catholicism in Vietnam has recently flourished, with more churches being built and congregations growing.
Catholic iconography is freely on sale in every corner of the country.
With more than six million believers, Vietnam boasts one of the largest Catholic communities in Asia and the Vatican wants to maintain its influence in the country.
It also wants to be able to appoint priests without state involvement.
President Triet's 40-minute meeting with Pope Benedict XVI on Friday was hailed by both sides as a "significant step" towards normalising relations.
After the meeting, a statement said the Holy See "expressed the hope that outstanding questions may be resolved as soon as possible".
Rising hopes
There is widespread hope among Vietnam's Catholic community that after President Triet's visit Vietnam and the Vatican would normalise relations and that would help settle land disputes in a more acceptable manner.
They also hope that the Pope will pay a visit to Vietnam in the near future. Official diplomatic ties between the Vatican and Vietnam would help bring this about.
Bishop Peter Nguyen Van Nhon, President of the Episcopal Council of Vietnam, said in an interview with the Vatican's news agency Fides that the meeting between Mr Triet and the Pope could create a "useful exchange".
"Exchanging information leads to mutual understanding to bring promises and new hopes to Vietnam and to the Church," Father Nhon was quoted as saying.
Vietnam's conditions
However, Hanoi seems unhurried and may have more say in the matter than it used to.
The Holy See made it clear during an Ad Limina (reporting) trip by Vietnamese bishops last June that the Church does not wish to replace a responsible government. But it is not enough.
Vietnam wants ties with the Vatican for international recognition, but wants its church leaders to follow Vietnam's rules, not the Vatican's.
As explained by Nguyen The Doanh, the former head of the Government's Religious Committee, a normal relationship can only be achieved when the Vietnamese Catholic church and the Vatican are "in sync".
"The Vatican has shown very good will. But it (normalisation) also depends on the behaviour of the Vietnamese Catholic church," he said.
"Unfortunately there are still some priests in Vietnam who don't think the modern, advanced way," Mr Doanh told BBC.
One of them is Father Nguyen Van Ly, a dissident who has been in and out of prison in the last 25 years and is currently serving an eight-year sentence for spreading anti-government propaganda.
Hanoi also issued warnings to some of the priests who backed the land protests in 2008 and 2009, including the Archbishop of Hanoi, Joseph Ngo Quang Kiet.
Observers also note another factor that officials in Hanoi may be considering: China's approach to its own Catholic church.
Among Asian countries, only Vietnam, China, Burma, North Korea and Malaysia do not have diplomatic relations with the Vatican.
Some believe that Hanoi, always careful not to offend its big neighbour, is reluctant to close any deal before Beijing at least makes some move in its relationship with the Vatican.
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SIC: BBC