The Muslim Education Centre of Oxford (Meco) accused Witney-based Open Doors UK of preaching "evangelical propaganda", after the Christian group held a Call to Prayer day in Oxford yesterday.
But Open Doors UK, which held the event at St Aldate's Church, insisted it had been taken out of context, although it "regretted" any offence that had been caused.
A spokesman denied the meeting targeted Muslims, and said its aim was to reduce fear of Islam.
Meco chairman Dr Taj Hargey was invited on BBC Radio Oxford yesterday to talk about the month of Ramadan, and was followed on to Phil Mercer's show by Brother Andrew from Open Doors UK.
Dr Hargey said: "It was only then that I learned they were running a day-long Christian initiative called Call to Prayer.
"I was flabbergasted and straight away looked at their website. The innocent sounding publicity was headlined 'A Call to Prayer', but Open Doors goes on to call Islam an 'ideology'. I was shocked by their theological self-righteousness. They assume the self-appointed task to 'pray for Muslims'.
"They also say that each year there are incredible stories about how God answers these prayers, revealing Himself to Muslims around the world, and bringing many to faith in Jesus."
Dr Hargey also said the event was advertised with an image of a fully veiled woman, but less than one per cent of women in Oxford covered their faces.
He added: "Not only was this evangelical activity ill-conceived and insensitive, it was grossly insulting and inflammatory to Oxford's Muslim inhabitants.
"At Meco our aim is to bring people of all faiths together, not divide them further. Things like this only serve to break people apart."
Source: Oxford Mail (English)
See also: Praying for Muslims