Traditionally regarded as loyal to Assad, Christians are facing aggression from Islamist rebels, and, whatever their sympathies, are becoming a trapped minority in a disintegrating country

Syrian Christians like to say that they belong to an ancient community that long pre-dates the arrival of Islam – and that whatever the outcome of the uprising against President Bashar al-Assad, they will still be there when it is over. But these are deeply unsettling times – highlighted by the case of the two bishops kidnapped on Monday in another alarming example of the human toll of a war without end.

Bishop Yuhanna Ibrahim, head of the Syriac Orthodox church in Aleppo, and Bishop Boulos Yaziji, of the Greek Orthodox church in the city, were abducted by gunmen Syrian state media called "terrorists". Later the kidnappers were described as "Chechen mercenaries" fighting with Jabhat al-Nusra, an extreme Islamist group that has links with al-Qaida. The anti-Assad opposition countered at once that it believed the regime was implicated.

Christians make up about 10% of Syria's 23 million population and have traditionally been regarded as loyal to a regime that strictly limited political freedoms for all citizens but guarantees their religious worship. Like other minorities, they have been mainly neutral or loyal to Assad since the uprising began two years ago. Still, an estimated 300,000 have already fled abroad.

Samir Nassar, the Maronite archbishop of Damascus, warned dramatically earlier this month that Christians in Syria now faced a choice between "two bitter chalices: to die or leave".

The church hierarchy is generally cautious. "We Christians are citizens like all other Syrians," Bishop Loukha al-Khouri, deputy patriarch of the Greek Orthodox church – the largest denomination – told the Guardian in Damascus last week. "We live in freedom and carry out all our religious ceremonies. The so-called opposition accuse us of defending the regime and the president. But as a church we respect our president and the government because they look after stability and security. Christians have been here since the days of St Paul. Syria is the best country for Christians in the region."

Christians serve in the armed forces and other security forces. Michel Aflaq, the founder of the Ba'ath party, was Greek Orthodox. Early on in the uprising, Assad appointed a Christian general, Daoud Rajha, as defence minister, but he was killed in a bombing last summer.

Still, there is no disguising a sense of growing anxiety against a background of allegations that churches have been attacked and Christians targeted by rebels.

But a church in Deir al-Zour in the north-east was hit by government air raids. Easter services had to be cancelled in Homs last year after weeks of heavy shelling. Bishop Ibrahim made waves recently when he said he could not blame so many Christians for leaving considering the "difficult circumstances in terms of security and the threats they face daily." He also rebuked the president for "not dealing with the crisis in a better way". Ibrahim is also said to have had good relations with the rebel Free Syrian Army (FSA) in the part of Aleppo under their control.

The Syrian National Coalition, the main western-backed anti-Assad grouping, has tried to avoid any whiff of sectarianism and has condemned Jabhat al-Nusra as "un-Syrian". Its current leader, the respected George Sabra, is a Christian. Abdulbaset Sieda, another opposition leader, is a Kurd. Other Christians such as Michel Kilo played a prominent role in the opposition long before 2011. Basil Shehadi, a young Christian film-maker and activist, was killed by a government sniper in Homs last year.

The bishops' abduction combines specific Christian concerns with the general phenomenon of lawlessness at a time when the regime is emphasising – critics say exaggerating – the Islamist aspects of the uprising.

Officials in Damascus focus sharply on Jabhat al-Nusra. Assad himself told a delegation of visiting Lebanese politicians on Sunday that the Syrian army was now facing "al-Qaida" and played down the role of the FSA. In recent days, state TV broadcast an interview with a captured Nusra leader who warned that Christians faced three stark choices: to convert to Islam, to pay a tax as a minority, or to be killed.

"Everyone is afraid of these extremists," said George Nashawati of the St Gregory Orthodox Society for Orphans and the Elderly in Damascus. "But especially Christians. Look what happened in Iraq. It could happen here."

However, a priest from Harasta described how Muslim neighbours had asked to shelter in his church during fighting. "Of course there have been some negative incidents but it would be wrong to give the impression that all Muslims behave like that," he added. Other Christians say that for all the deterioration in security they do not feel targeted because of their faith.

Bishop Khouri, who is known as an ultra-loyalist, accused western countries of betraying their own religious heritage by backing the rebels. "France likes to say that it defends Christians but they help terrorists to come to our country," he complained. "How is that Qatar can influence France and Britain with their money? It is well known that the leaders of Qatar are Jews."

Other Christians adopt a more nuanced position – sitting on the fence rather than standing on the front line. "In Syria there are moderate Muslims who don't discriminate against Christians," explained Abu Jean, a crucifix hanging prominently from the mirror of his Damascus taxi. "We are afraid of people like Jabhat al-Nusra. We will fight each other and we will suffer. Christians should be neutral. But this is not our business. I will not let my son join the [government] popular committees or the national defence army – or the armed opposition either."

• This article was amended on 26 April 2013. The original described the estimated 300,000 Christians who have fled abroad as "perhaps a third of the total".