Deutsche Presse-Agentur reports that the meeting also marks the yearly anniversary of the signing of the 1929 Lateran Pacts, which regulated dealings between the two sovereign states, and their subsequent revision, in 1984.
Relations between Prodi's centre-left government and the church hierarchy have been severely strained by a recent decision to grant new rights to de facto couples, including those of the same sex.
The 'rights of cohabiting people,' or 'DICO' bill was drafted in a special cabinet meeting held on 8 February and will now be submitted to parliament for approval.
But Pope Benedict has dismissed civil unions as 'pseudo-matrimony'.
A poll published on Monday by Corriere della Sera suggests Italians are split down the middle over the issue, with 45 per cent of respondents expressing support for DICOs, compared to 47 per cent of those against.
"We want dialogue and cooperation (with the Vatican) on the most important problems facing us, including the family and our bill draft," Prodi told Italian state television RAI.
Prodi was expected to hold talks with a Vatican delegation headed by the Vatican's Secretary of State Cardinal Tarcisio Bertone and the head of the Italian Bishops Conference Cardinal Camillo Ruini.
Italy's Prodi seeks to defuse gay unions row with Catholic Church (Monsters and critics, 19/2/07)
Pell opposes IR laws, supports same-sex union ban (CathNews, 19/6/06)
Washington Cardinal clarifies view on same-sex unions (CathNews, 14/6/06)
20 Feb 2007