Francis met Abbas at the Vatican on Saturday and used the words as he presented the Palestinian president with a large bronze medallion representing the angel of peace, one of his customary gifts to visiting presidents.
Receiving Abbas at the papal apartments, the Argentine pontiff, speaking in Italian, said the medallion was an appropriate gift because "you are a bit an angel of peace", according to a reporter representing several news agencies at the meeting.
Vatican spokesman Federico Lombardi said he had not heard the remarks himself and had nothing to add to the words attributed to the pope by the pool reporter.
"It is clear that there was no intention to offend anyone," Lombardi told Reuters.
Early reports had conflicted as to whether the pope urged Abbas to be an "angel of peace" or if he had described him as such.
The pope met Abbas a few days after the Vatican formalized its recognition of the Palestinian state, a move which riled Israel's government.
The Vatican said after Saturday's meeting that the two had expressed hope that talks between the two sides could resume after breaking down a year ago.
Francis and Abbas, who met last year with former Israeli president Shimon Peres in an unprecedented inter-religious event at the Vatican, had a "very colloquial" exchange as they exchanged gifts, Lombardi said in a statement.
"In any case, the sense of encouraging a commitment to peace was very clear and I believe that the very gift of the symbol of an angel of peace was made by the pope with this intention as well as previous presentations of the same gift to presidents, not only to Abbas."
Lombardi said the pope explains the significance of the medal to heads of state who receive it, and that the word "angel" in this context means "messenger".
Abbas also attended a canonization ceremony on Sunday at which Francis made saints of two Palestinian nuns.