Juncker's Christian Social Party, aided by the Church in the country, attempted to block the legislation allowing for euthanasia, but the bill passed 30-26 in a vote in Parliament last month.
The bill still needs to pass a second reading for it to become law. The measure is expected to pass and could come into force before summer.
Luxembourg, a country of some 480,000 people, 87% of whom are Catholic, is the third country of the European Union to legalize Euthanasia. Holland was the first to do so in 2002, and Belgium followed suit in 2003.
Under the law, doctors are allowed to help terminally ill patients to end their lives, but only under the condition that the patient has made repeated requests, and with the consent of two doctors and a panel of experts.
During the nearly 30-minute meeting, the Vatican communiqué said "the cordial discussions provided and an opportunity to evoke the good relations that exist between" the Vatican and Luxembourg, "and to examine a number of questions of mutual interest concerning the current situation of the country."
"Attention also turned to the international situation," the note said, "in particular to the future of Europe, to the Middle East and the presence of Christians, to conflicts in various parts of the world and to interreligious and intercultural dialogue."
The Luxembourg leader met afterward with Archbishop Dominique Mamberti, secretary for relations with states.