The powerful Orthodox church on the Mediterranean island of Cyprus has been embroiled in a scandal involving two monks accused of fraud.

Cypriot police are investigating events at Osiou Avakoum monastery, located in the picturesque village of Fterikoudi in the foothills of the Troodos mountains, after allegations against the now-suspended clergymen were first made public by a leading bishop earlier in March.

CCTV footage leaked to local media appeared to show the two men plotting to trick parishioners into donating money to the church by secretly placing myrrh inside a metal cross to make it seem as if it were bleeding.

They were also reportedly caught on camera engaging in sexual activity with each other. Same-sex relations are frowned upon by the church.

Both monks had been active on social media for some time with posts claiming to have seen various "miracles" like curing cancer, a deaf baby regaining its hearing and infertile couples unexpectedly bearing children.

Some 800,000 euros in cash was also reportedly found in a safe at the property earlier in March during a raid ordered by Bishop Isaias of Tamassos, who has direct authority over the monastery.

Thousands of faithful had been drawn to the monastery from across the island and were strongly encouraged to make donations.

Police spokesperson Christos Andreou told local media they were investigating "crimes of a financial nature by the Osiou Avvakoum monks", as well as a complaint by the men who say they were kidnapped by hooded men during the church raid.

Andreou declined to provide further details when contacted by AFP due to the ongoing inquiry.

No formal charges have yet been brought, and the Greek Orthodox Church of Cyprus is conducting its own investigation.

The men are now due to appear in May before the Holy Synod, the church's decision-making body, after Orthodox Easter in late April, when they could be defrocked or excommunicated.

In a statement, church head Archbishop Georgios expressed his "sincere regret regarding the revelations of alleged fraud, misconduct and all kinds of immorality within the ranks of the Church of Cyprus".

He told Greek newspaper Kathimerini "there can be no marketing or selling of either holy relics or miracles", acknowledging the church must take stricter measures.

The Orthodox Church retains a strong conservative influence on social and political life in Cyprus and is a major economic player, with vast land holdings and stakes in beverage, banking and other sectors.

"The real scandal is the complete lack of transparency when it comes to the Church of Cyprus finances," Cyprus lawyer Michalis Paraskevas told AFP.

"As far as we know, there is no regulation whatsoever on which activities of the church are being taxed or not, and how much of their money comes from donations and how much from business activities," he added.