The head of Egypt's Coptic Church, Pope Tawadros II, has shut down his Facebook page, saying it was a "waste of time", after the church ordered monks off social media.

State-run Al-Ahram newspaper said on Saturday that Tawadros's decision was in line with a dozen measures announced Thursday by the church relating to the activities of monks.

One of the measures gave monks a month "to deactivate and close any social media pages or accounts and voluntarily renounce these behaviors that are not true to monastic life".

On Thursday the church also said it will stop accepting any new monks for a year after the mysterious death of a bishop at a monastery northwest of Cairo.

In his last posting on Facebook before shutting the page, Tawadros said that using social media is a "waste of time, age and life".

"That is why I am shutting down my personal Facebook page and I salute all my brothers and sons who have followed the instructions of my sacred church".

According to Al-Ahram, several senior Coptic Church officials have followed Tawadros' example and shut down their Facebook pages.

Tawadros became pope in 2012, and according to Egyptian media has not been active on Facebook since he opened his page in 2009.

Coptic Christians make up about 10 percent of Egypt's predominantly Sunni Muslim population of 100 million.

Meanwhile Egyptian police continue their investigation into the death of Bishop Epiphanius, the 68-year-old abbot of Saint Macarius monastery in Wadi el-Natrun, who was found with head injuries on Sunday.

A security official has said his death was being investigated as a possible murder.