He promised that "change will not be stopped" as he delivered the key address of his party's annual Ard Fheis in Wexford.
"Let's be clear," he said. "Issues like Acht Na Gaeilge [Irish language act], a Bill of Rights and the Long Kesh site, are not going away. Let us also be clear. These issues will be resolved. So too will issues of identity and contentious Orange parades.
"While there may be obstacles, be sure of one thing - change will not be stopped.
"I am happy to meet with the Orange Order at any time to discuss these matters."
Dealing with contentious parades was one issue which former US diplomat Richard Haass and Professor Meghan O'Sullivan failed to reach agreement on last year with Stormont's politicians, but Adams acknowledged the progress made.
The Louth TD said he wanted to see the Orange Order treating its Catholic neighbours with respect.
"I want to see it upholding law and order," he added.
"The Orange Order of Ireland is one of our national traditions.
"Orange is one of our country's national colours.
"And Sinn Féin wants all our traditions freed up from sectarianism from any quarter, to live together in peace and respect and with tolerance from everyone for everyone.
"The tide of history is with those who seek to build a peaceful and inclusive future. And Ireland, north and south, is changing."
His speech, however, was largely dominated with southern issues.
The renowned artist Robert Ballagh has said that this Government is one of the worst for the arts in the history of this State. Robert Ballagh is right.
Mr Adams said that the society has become increasingly polarized between 'haves' and 'have nots', ruled over by a Government which is increasingly arrogant.
He also touched on immigration, explaining that 10 people were leaving Ireland's shores every hour - 240 people a day.
"That is 240 devastated families.
"Enda Kenny, our Taoiseach insults all of these families when he dismisses this as the desire of young people to travel."
He continued: "For some parents, all their children have left. They are the Skype generation, the scattering -- given a final push out of the country by targeted dole cuts and the exploitation of Jobsbridge.
"These 400,000 people and their families know exactly who is responsible for their forced emigration.
"That's why there is no Government Taskforce on emigration.
"That's why there is no vote for the diaspora that would give them a stake in our country."
The Sinn Féin leader also attacked the health service in the Republic, saying his party firmly stands for a national public health service and called for the current Health Minister James Reilly - and the government - to go.
"This state's two-tier health service is at breaking point. We oppose cuts to the health budget and support all those who are making a stand.
"Like communities where the absence of a proper ambulance service is the difference between life and death.
"Like patients waiting years for procedures because there aren't enough nurses and doctors to cope with the demand."
UTV's Political Editor Ken Reid said: "This was a pretty low key Ard Fheis, but I think it will be remembered for the fact that any doubts about Gerry Adam's leadership have been firmly removed.
"He had a standing ovation even before he took to the stage, and then afterwards there were three or four minutes of another standing ovation. Now that's despite the fact that there's been controversy over his brother's conviction, there's been controversy over the Disappeared.
"But there's no doubt that Gerry Adams is very much in charge of Sinn Féin."
Regarding his offer to meet with the Orange Order, Ken Reid said: "He has said this before - that he has been willing to talk to the Orange Order. Perhaps what I take from the speech is a large proportion of the speech was actually about southern politics and it's an indication of where the thrust of the Sinn Féin agenda is going at the moment.
"And in some ways, there was just a passing mention of Northern Ireland."