But the decision by the church's 12-member governing body, the Holy Synod, noted the ``justified'' opposition by some followers and insisted any papal trip remain strictly a pilgrimage to Biblical sites.
The visit would likely come in early May as part of a planned trip to Syria and Malta. The 80-year-old pontiff expressed interest in including Greece in order to follow the steps of the Apostle Paul.
However, Greece's clerical union predicted massive protests would greet the pope, who they described as the ``arch-heretic'' and ``two-horned grotesque monster of Rome.''
``Parish priests and the devout public wash their hands of anything that will happen during the visit,'' said the Rev. Efstathios Kollas, president of the union that represents about 8,000 Orthodox parish priests. There are fears that monks from the all-male monastic community of Mount Athos could join any protests, giving them a connection to one of the most respected centers of Orthodoxy.
Holy Synod spokesman Metropolitan Efstathios said police and security services in Greece and at the Vatican had been warned about the possibility of problems.
Despite the threats, the Vatican reacted positively to the Greek church's announcment. The decision to accept the pope as a pilgrim to Biblical sites ``meets the holy father's expectations,'' said Vatican spokesman Joaquin Navarro-Valls. He said the pope was grateful.
The spokesman said an announcement about the actual trip could come soon.
``In the broader spirit ... the church does not want to say no to the pontiff especially since the trip has the character of a pilgrimage and only that,'' said a statement approved unanimously by the 11 Synod members present.
The overture could be a major step toward healing the ``Great Schism'' that split the Christian world into Orthodox and Catholic branches nearly 1,000 years ago.
Greek Catholics welcomed the decision, which would mark the first-ever visit to Greece by a Roman Catholic leader.
``The decision of the Holy Synod can open a new page in the relationship between the Greek Orthodox Church and the Catholic Church. With sincere love, at some point the two churches must discuss positively about the complaints and the misconceptions that exist on both sides,'' said Nikos Gasparakis, a spokesman for the Roman Catholic Church in Greece.
The Church of Greece is considered among the most conservative of the various ethnic and national churches in Orthodoxy and its clergy view themselves the protectors of the faith.
The Greek government has already extended an invitation for the pope to visit Greece as a head of state. But the pope is thought to have also wanted the agreement of Greece's powerful church.
The Greek church last year rebuffed the pope, demanding an apology for what it considers a long history of Vatican-sponsored aggression and arrogance.
Some liberal Orthodox clergymen see the pope's impending visit as helping heal the estrangement between Roman Catholics and Orthodox. But many Greek Orthodox factions hold strong anti-Vatican views.
Another main dispute is over the role of Eastern Rite churches, which follow Orthodox traditions and trappings but are loyal to the pope. Some Orthodox clergymen claim the Vatican is using Eastern Rite followers to encroach on historic Orthodox lands.
There are only about 50,000 Roman Catholics among Greece's 10.2 million native-born population. But there are tens of thousands of Roman Catholic immigrants.
A visit to Athens could also influence the stand of the Russian Orthodox Church - considered equally conservative - and possibly pave the way for a papal trip to Moscow. In 1999, the pope visited predominantly Orthodox Romania and Georgia. He is scheduld to visit mostly Orthodox Ukaine in June.
Russian Patriarch Alexy II has said a meeting with the pope would be possible only if disputes between his church and the Roman Catholic Church are resolved. In the past, Greece has stringently supported the Russian church's views.
Current Russian Orthodox-Vatican disputes are twofold. The Orthodox claim Catholic missionaries are seeking converts among the traditionally Orthodox Russian population. The two churches are also fighting over formerly Orthodox properties that were ceded to the Orthodox under communist rule.
The up coming papal visit to Ukraine has added fuel to the controversy. Just Tuesday, Alexy II again said he thought the planned visit was premature and should be postponed.