He went voluntarily to Newtownabbey PSNI station on Friday morning. Police enquiries are continuing.
Earlier, he apologised for any distress caused by a sermon during which he described the Islamic faith as "heathen" and "satanic" and "spawned in hell".
The evangelical Protestant preacher likened "cells" of Muslims in Britain to the IRA as he addressed a congregation at Whitewell Metropolitan Tabernacle in north Belfast last month.
A statement has been posted onto the church's website, which reads: "I wish to make a clarification statement with regards to statements made by me recently in relation to members of the Muslim faith.
"I wish to emphasise that I had no intention of causing any offence or insulting any member of the Muslim community or to arouse fear or stir-up or incite hatred towards any member of the Muslim community."
He added: "My sermon was drawing attention to how many followers of Islam have, regrettably, interpreted the doctrine of Islam as justification for violence.
"I have qualified my comments by reference to those who use their religion as justification for violence. As a preacher of the word of God, it is this interpretation of the doctrine of Islam which I am condemning.
"I abhor violence and condemn anyone, of any faith, who uses religion to justify it."
I wish to apologise publicly for any distress I may have unwittingly caused on my part.
Pastor McConnell said that he had devoted 60 years of his life to the service of God and preached the word of God as a Pastor to thousands of people.
"I have worked tirelessly to promote my Christian doctrine. Many faiths and denominations have attended at the Whitewell Metropolitan Tabernacle, including members of the Muslim faith.
"My mission has created a community in Ethiopia which ensures over 600 children a day, including Christians and Muslims, have access to clean water and food. In addition, we fund a clinic in Kenya which provides 1200 people a month with access to medical care."
He added: "I believe in the principle of free speech and in freedom of religion.
He said he will "welcome any opportunity to attend at the Islamic Centre in Belfast in the near future".
Islamic representatives have welcomed the preacher's apology.
Spokesman for the Belfast Islamic Centre, Dr Raied Al Wazzan said: "The apology is definitely welcome.
He added: "The current issue caused some race relation problems and we need to work to heal that, so we still have to do some work, maybe we can come together and show solidarity with each other and support each other."
Yes, it is three weeks late but late is better than never and we do accept his apology
Dr Raied Al Wazzan
Pastor McConnell has offered to visit the Belfast Islamic Centre in his statement of apology.
Dr Al Wazzan said he would welcome the minister to the centre.
"He is very welcome like everybody else," he said.
"The Belfast Islamic Centre is open doors for anybody who wants to come to listen to our faith and see what we believe in - everybody is welcome."
A PSNI spokeswoman said: "Police have interviewed a 77-year-old man and continue to investigate offences connected to a number of allegations of race related crimes.
"Upon completion of those investigations, police will submit a file to the Public Prosecution Service."
The pastor's sermon was condemned by Stormont's deputy First Minister Martin McGuinness, at the time, who described it as "irresponsible".
Other politicians condemned the remarks, as did representatives of the Muslim community in Northern Ireland.
However, First Minister Peter Robinson initially defended the evangelical pastor in an interview with the Irish News.
The DUP leader said it was "the duty of any Christian preacher to denounce false doctrine".
The politician, who attends the church in question, added: "He's perfectly entitled to do that - it's an appropriate thing for a minister to do."
Mr Robinson said he did not trust Muslims who were involved in "terrorist activities" or those "fully devoted to Sharia law".
In a later interview with UTV, Mr Robinson said he stood by the comments and that his interview had been taken out of context.
However, he has since publicly apologised and visited the Islamic Centre in Belfast earlier this week.