He told about 1,000 republicans gathered for an anti-internment rally in Belfast city centre that he would not "put some version of words together to satisfy Unionism".
Demands have been growing for Mr Adams to declare that the IRA's campaign is over for good. But he said: "I'm under no pressure. Let no one preach to any republican that we have to say this, or we have to say that, or we have to put some version of words together to satisfy Unionism.
"We want to make peace with the Unionists, but we cannot resolve David Trimble's problems for him. He has to talk to us and accept that we need to be treated in the same way as he wants his supporters to be treated."
Mr Adams' comments came as political leaders in Northern Ireland gave a cautious welcome to a pledge by the Loyalist Volunteer Force that it was ending its campaign of violence.
The organisation, responsible for a series of sectarian murders of Catholics, declared it was calling "absolute, utter finish" to the violence.
Just before the referendum on the Good Friday agreement, the LVF, whose leader Billy Wright was assassinated in the Maze prison, called a ceasefire. However, its prisoners were not among those included in the early release scheme for paramilitary prisoners.
The latest move is seen by most observers as an attempt to get those inmates out. But the group is regarded as so unpredictable and ill-disciplined that the statement may not be enough. "It is in the prisoner release legislation that the LVF will not benefit. If that is to be changed it will probably be up to deeds, not words, and one of the major deeds is giving up weapons," said a government source.
In a statement the LVF said: "Irrespective of whether or not republicans recognise the English dictionary, for LVF personnel the meaning of the word `complete' is quite clear. The word means; entire, whole, brought to an end, perfect, absolute, utter, finished."
Mo Mowlam, Secretary of State for Northern Ireland said she welcomed the statement but added that it was important the LVF maintained a complete and unequivocal ceasefire.
Despite having agreed to call off its campaign, LVF members were blamed by police for the violence at last month's stand-off at Drumcree, and they were also suspected of involvement in arson attacks on a number of Catholic churches.
Ken Maginnis, of the Ulster Unionist Party, said: "I would welcome any declaration of non-violence. Let's just hope they have the courage to see it through."
However, another loyalist politician, Billy Hutchinson, of the Progressive Unionist Party, was less impressed. He said: "I think it's a bit ironic that these are the people to claim that myself and others sold out and now we have got them saying it's OK to declare the war is over. These people are gangsters, drug dealers and informers."
It has also emerged that the Government has been in unofficial contact with the republican terrorist group, the Irish National Liberation Army, which has not declared a ceasefire. However, official sources said the discussions were at a very early stage and there was no question of INLA prisoners being released early.
The Northern Ireland Office stated that the cost of resettling paramilitary prisoners released early could come to pounds 3,000 each. About 400 inmates are expected to be released in the next two years.
A spokeswoman denied that the prisoners would be given cash sums to help them adjust to life outside.
She said: "Like any other serving long sentences they would go through a pre-release scheme which could involve counselling and training. The cost of all that preparation could be in the region of pounds 3,500 but they are not going to get large cheques in their hands."
In overnight violence on Saturday, police were attacked with petrol bombs in Strabane, Co Londonderry. Two women, one a police officer, were injured and baton rounds fired.
Earlier, the annual Apprentice Boys' march in Londonderry led to clashes between loyalists and nationalists in which two police officers suffered serious injuries. The Apprentice Boys accused nationalists of breaking a peace agreement and carrying out an unprovoked attack on the march. Alistair Simpson, governor of the Apprentice Boys, said: "The republican movement collectively used hype and misrepresentation. The sectarian hatred is an obvious consequence of such an irresponsible approach."
Mr Hutchinson, of the PUP, is scheduled to have talks today with the Northern Ireland security minister, Adam Ingram. He said: "The republicans seem to be getting everything their own way and loyalists are not getting anything. This [Apprentice Boys] parade should never have been the subject of negotiation in the first place. I am just tired of the Government giving in to republicans."Reuse content