A Christian father and son have been shot dead by an Egyptian police officer, according to International Christian Concern (ICC).

Coptic Christians Imad Kamal Sadeq, 49, and his son David, 21, were shot by Robi Mustapha Khalifa, who was stationed as a security guard at the Nahded-al-Qadasa church in Minya, Upper Egypt.

He is in custody being questioned while authorities reviewed CCTV footage from the church's security cameras.

Citing a local source, ICC said the two men were engaged in construction work on their nearby home and a dispute arose between them and Khalifa, who had refused to move his motorbike when they asked.

Video footage of the December 12 incident posted on social media shows that the police officer walked over to the men's home with his weapon drawn. After what appears to be a brief conversation, they were shot in the street.

A local Christian told ICC: 'A day before the incident, the killer had threatened them. Their family is now ruined [homeless].'

The funeral was held on Thursday at Minya's St Bishoy and St Paul Coptic Orthodox Church and was attended by thousands of people who protested against the lack of protection offered by the state.

Witnesses described angry exchanges between some 2,000 mourners and policemen guarding the funeral in Minya.

'One, two, where are the rights of the martyrs?' the crowd chanted.

The head of the local diocese, Archbishop Macarius, who led the funeral prayers, demanded a response from authorities.

'We call for all armed police officers assigned to guard churches to be checked. Are they qualified to carry live ammunition, so that they don't become a source of danger rather than protection,' Macarius tweeted.

He also urged President Abdel Fattah al-Sisi to intervene personally to tackle the poor healthcare, education and employment prospects of Christians and Muslims in Minya.

Copts, who make up around 10 per cent of the population, have long complained of discrimination. They have also frequently been attacked by Islamist militants who see them as infidels, prompting authorities to place armed guards outside churches and monasteries.

Last Wednesday's killing angered local Copts still reeling from the death of seven members of their community in an Islamist militant gun attack in November.

Claire Evans, ICC's regional manager for the Middle East, said: 'It is extremely worrying that a police officer, one specifically tasked with the security of a church, would be the perpetrator of such a violent act of persecution against Christians. Historically, the authorities are rarely held accountable for using their position to harass, intimidate, and even attack Christians. Tensions in Minya remain high as Christians are extremely concerned that they will be further singled out by the local authorities. We must keep Egypt's Christians, and specifically the victims' family, in our prayers.'

Additional reporting by Reuters.