He said they wanted conflict in Ireland ended forever: 'All armed actions must end. The prisoners must go free.'
The traditional republican anti-internment march was also designed to mark the 25th anniversary of the arrival of British troops on the streets. It was slightly less well-attended than a similar march several months ago.
Although Mr Adams's speech seemed to break no new ground, the expectation is still widespread that the IRA is on the verge of declaring a substantial ceasefire, probably next month. Republican sources are making little attempt to deflate the near-universal speculation that a ceasefire is on the way.
They say that a meeting between Mr Adams and the leadership of the IRA has left them hopeful that significant movement is possible. But they also caution that certain conditions have yet to be met before everything falls into place.
'Nobody has signed up for anything yet,' one source warned, while declining to elaborate on what the conditions might entail.
The sources are emphatic that there is no contact, direct or indirect, between the republican movement and the British government. But there is no such denial of contacts with the Irish government, and it is widely believed that meetings have taken place between Dublin representatives and Sinn Fein councillors.
One source said: 'There is a lot going on beneath the surface, but it is just far, far too sensitive for us to talk about at the moment. We are cautiously hopeful, though.' In his speech Mr Adams declared: 'We are told Britain has no selfish interest in being here. Well, if Britain has no interests then the British troops must go, the Unionist veto must go, partition must go and all that is unjust and discriminatory must go.'
The RUC said yesterday that a Catholic man shot dead by loyalists early yesterday 'obviously went through hell before he died'. The body of Sean Monaghan, 20, from the Falls district of Belfast, was found gagged and bound in the Shankill area. The RUC said it had been 'a horrendous sectarian murder of a quiet, timid man who lived only for his girlfriend Noelle and their 15-month- old twin daughters'.
A police spokesman described the killers as 'sick, pathetic thugs'. Mr Monaghan, who lived in Albert Street, visited an uncle at Divis Towers on Saturday night but left shortly after midnight.
He had to walk only a short distance to his own home but is thought to have been captured by a gang prepared to kill any Catholic it could abduct.
In a telephone call later to the BBC, the outlawed Ulster Freedom Fighters claimed they had 'executed' a 'republican spy'.
However, the caller named the victim as Sean Mulligan - suggesting that the assassins may not have checked the man's identity.
Alex Attwood, a Belfast SDLP councillor, described the murder as part of a 'highly organised and systematic targeting of Catholics in Belfast'.