During the meeting the two sides discussed values in today's society, and facing different challenges, a statement from the presidential press office said. Following some rather glum-faced recent encounters, the Pope even managed a beaming smile.
The President invited His Holiness to visit Latvia next year, to mark the centenary of the country's founding.
"Latvian as a multicultural country has a diversity of religions, and conducts successful cooperation between the different Christian confessions," Vejonis said, citing the multi-denominational Taizé meeting in Riga at the end of 2016.
"Ecumenicalism is therefore a good basis for the integration of society," said Vējonis, adding that the visit of Pope John Paul II to the Baltic States in 1993 is still remembered as an important event.
The meeting also discussed current international issues including the need for action on environmental protection and climate change prevention - on the same day the US' President Donald Trump announced his country would join Syria and Nicaragua by pulling out of the Paris Climate Agreement.
The President also expressed his gratitude for the fact that the Holy See has always supported the efforts of Latvian independence and never recognized the incorporation of Latvia into the Soviet Union.
Through the darkness of today's conflicts, every one of us can become a bright candle, a reminder that light will overcome darkness.— Pope Francis (@Pontifex) June 2, 2017