By Agence France-Presse
The two men "discussed the good relations which exist between the Holy See and Vietnam, reinforced by a common spirit of dialogue" over the course of a 15-minute meeting Wednesday, the statement said.
The Vatican said the states were "constantly searching for ways to develop relations even further", but did not comment on the possible re-establishment of diplomatic ties.
Vietnam's communist regime broke off diplomatic ties with the Vatican in 1975, but both sides have been working towards reconciliation since 2007, including a meeting between the prime minister and the pope two years ago.
The papal nuncio in Singapore, Leopoldo Girelli, has been the Vatican's "non-resident pontifical representative" to Hanoi since 2011.
The vast majority of Vietnam's 93 million inhabitants say they follow Buddhist traditions, but about seven percent of the population say they are Catholic.
Catholic land confiscated since the end of French colonial rule in 1954 remains a contentious issue between the church and state, and has led to demonstrations.
In recent years, church leaders have also called for jailed activists to be released from prison and have fought for religious freedoms in the authoritarian nation.
The pope is keen for the Church to tap into Asia, a continent where the number of Catholics, currently just 3.2 percent of the population, is rocketing.
Since becoming pope in 2013, Francis has visited South Korea, Sri Lanka and the Philippines, and is working towards a historic reconciliation with communist China.