The Sinn Féin president also challenged Democratic Unionist leader the Rev Ian Paisley to face to face talks in a bid to revive Northern Ireland's power sharing administration.
Mr Adams claimed the IRA's decision to abandon its armed campaign created an unparalleled opportunity which must be grasped by all sides involved in the political process.
Even though terror bosses within the main protestant paramilitary organisations have pledged to retain their weapons, the West Belfast MP insisted it was time to leave violence behind.
He said: "I would like to think that as the import of the IRA's decision starts to play out, sensible people within loyalism will follow the example.
"Sensible people within all those other armed groups will take pause for thought on these matters."
Despite Thursday's declaration by the Provisionals that it will now follow a purely political and democratic process, Mr Paisley and his senior party colleagues demanded action rather than words.
A major new push by the British and Irish governments to restore devolution in Northern Ireland could now depend on the DUP and Sinn Féin agreeing to work together.
Although Mr Paisley has refused to enter any direct negotiations with republicans, Mr Adams claimed Unionists now faced a responsibility to work together.
"They need decisive leadership and that's for Ian Paisley and his colleagues to come to terms with," the Sinn Féin leader said.
"I believe it's now time for dialogue between us."
Yet for one of the highest profile victims of republican violence, developments in Belfast and Dublin could not diminish the pain.
Tory peer Norman Tebbit was injured and his wife paralysed in the attempt to wipe out Margaret Thatcher and her cabinet by blowing up Brighton's Grand Hotel in 1984.
Five people died in the blast and Tebbit said yesterday: "For the terrorists' victims, there's the knowledge that their lives were not wrecked by illness, accident or even personal grudge but because someone used their lives, their bodies, to bludgeon and blackmail a government to submit to their political demands.
"We the victims should not have to endure the sight of terrorists rewarded nor fanatics left free to urge their followers to kill their way to paradise. That is just too much to bear."