The talks in Ramallah were co-chaired by Msgr. Ettore Balestrero, the Vatican undersecretary for relations with states, and Ziad al-Bandak, the Palestinian presidential adviser for Christian relations.
The Palestinian side gave the Vatican its response to a draft proposed earlier by the Vatican, the statement said.
"The talks took place in a positive atmosphere to strengthen further the special relations between the two sides," it said. "The delegations agreed to set up technical teams to follow up on the draft" in preparation for a larger meeting that will be held at the Vatican "in the near future."
Jesuit Father Federico Lombardi, Vatican spokesman, would not provide further details, but said the meeting was "a positive sign of good will."
The talks are aimed at providing concrete details for implementing the "Basic Agreement" signed by the Vatican and the PLO in 2000 spelling out principles for guaranteeing church rights and religious freedom in territories administered by the Palestinian Authority.
For years the Vatican has been engaged in similar discussions with the government of Israel. Talks continue, particularly on issues dealing with finances and taxation of church-owned property.