The verses were read at St Mary's Episcopal Cathedral on January 6 to mark the Feast of the Epiphany but sparked criticism.
One line, read in Arabic, states that Jesus is not the son of God and he should not be worshipped.
Church Primus, Most Rev David Chillingworth, wrote in an online post that the church is committed to interfaith development and will meet with those involved.
He said "the Scottish Episcopal Church is deeply distressed at the widespread offence which has been caused", but he did not apologise.
Instead he said the "decisions which have led to the situation in St Mary's Cathedral are a matter for the provost and the cathedral community".
For its part the cathedral has gone to the police, angry at online criticism it has received. Police Scotland said it was reviewing comments that had been reported as "offensive".
Rev Chillingworth wrote: "Those who seek to work in the area of interfaith relationships must weigh carefully whether the choices which they make are appropriate or otherwise.
"In today's world, those judgments must give careful consideration to good relationships which have been carefully nurtured over many years in a local context.
"They must also weigh carefully the way in which national and international issues shape perceptions of what is appropriate or inappropriate
"The decisions which have led to the situation in St Mary's Cathedral are a matter for the provost and the cathedral community but the Scottish Episcopal Church is deeply distressed at the widespread offence which has been caused.
"We also deeply regret the widespread abuse which has been received by the cathedral community.
"In response to what has happened at the cathedral, the Scottish Episcopal Church will bring together all those who are involved in the development of interfaith relations.
"Our intention will be as a church to explore how, particularly in the area of worship, this work can be carried forward in ways which will command respect."
