The group apologised for causing the casualties, saying the large car- bomb had been aimed at a commercial target rather than at taking life.
The statement follows calls from Sinn Fein saying those responsible for the devastating explosion should admit that they were involved. The statement was telephoned to the Dublin office of Belfast's Irish News newspaper by a caller using a recognised codeword.
It read: "This is about the explosion. This is Oglaigh na hEireann [IRA]. There were three warnings and there were 40 minutes' warning on each of them - two to UTV and one to the Samaritans in Coleraine. Each time this was made clear and people talked back.
"The location was 300 to 400 yards from the courthouse on the main street. At no time was it said it was near the courthouse. It was a commercial target. Despite media reports it was not our intention at any time to kill any civilians.
"It was a commercial target, part of an ongoing war against the Brits. We offer apologies to the civilians."
Mo Mowlam, Secretary of State for Northern Ireland, condemned the statement as a "pathetic attempt to apologise for and excuse mass murder". She said Real IRA members were "murderers pure and simple" and people would have "absolute contempt" for their apology.
The Real IRA, a breakaway from the mainstream IRA organisation, had emerged as the prime suspects for the attack within hours of the bombing on Saturday. As the days passed the authorities became satisfied that the bomb was planted by the group.
The statement therefore contained nothing of real surprise to the security forces on both sides of the border. The British and Irish governments and police forces have been formulating a security response to the attack, which is based on the premise that the group was to blame.
The Real IRA is said to consist of fewer than 100 activists, most of whom are based on the southern side of the border. Its members are thought to be concentrated in and around the border town of Dundalk in Co Louth.
The debate continues in political circles and elsewhere as to whether the Omagh attack was deliberately intended to take life. Those who believe it was not point out that in the wake of the killings the group has become "red-hot" in that it is completely isolated. Bertie Ahern, the Irish Prime Minister, has spoken of moving "ruthlessly" against it and of "crushing" the organisation.Reuse content