Mr Adams, a reputed IRA commander since the mid-1970s and leader of the province’s main Catholic party, stated he was no longer prepared to defend the IRA’s armed struggle.
In a keynote address on the second day of the British election campaign, he said it was time to rebuild the peace process and move the group’s struggle forward.
”In the past I have defended the right of the IRA to engage in arms struggle,” he said.
“I did so because there was no alternative for those who would not bend a knee, or turn a blind eye to oppression, or for those who wanted a national republic. Now there is an alternative.”
He acknowledged international public opinion had turned against the IRA.
But he didn’t directly call for the outlawed organisation to disarm fully and disband as the British, Irish and American governments have repeatedly demanded.
“The way forward is by building political support for republican and democratic objectives across Ireland and by winning support for these goals internationally,” he said.
“I want to use this occasion therefore to appeal to the leadership of (the IRA) to fully embrace and accept this alternative. Can you take courageous initiatives which will achieve your aims by purely political and democratic activity?”
The British Government cautiously welcomed the speech, labelling it as significant while the Irish Prime Minister Bertie Ahern said the appeal was “significant and has potential”.
But Protestant factions in Northern Ireland remain adamant a lasting peace settlement can only be achieved when the IRA ends all criminal and paramilitary activity.
The IRA declared a ceasefire against British rule in 1997, a decision that paved the way for a Protestant-Catholic power-sharing assembly.
But it was suspended more than two years ago amid allegations of IRA espionage, while violence persists in the form of punishment beatings, stabbings and shootings.
The IRA has come under heavy pressure since it was accused of involvement in a spectacular pre-Christmas bank robbery in Belfast and several of its members were linked to the January murder of Robert McCartney, a local Catholic man.
Criticism has also come from US President George W Bush and even Irish-American supporters, some of whom have called for the IRA to be disbanded.