The Sinn Féin MLA was speaking at his party's AGM in Omagh, Co Tyrone on Saturday.
He also praised Peter Robinson's leadership over the Stormont House Agreement.
Mr McGuinness said: "Sinn Féin has emerged from the recent negotiations in a stronger position.
"Our defence of the most vulnerable and our opposition to austerity - whether it is spawned in London or Dublin - was vindicated."
He continued: "The Stormont House Agreement was the best deal possible but, like all agreements, it is the implementation which will tell the story.
"We are now in that phase and we have made a good start and I want to recognise the positive leadership of Peter Robinson in making and adhering to the agreement.
"Over the coming period we are facing three crucial elections at Westminster, the Assembly and the Dáil.
"These elections give us the opportunity to take more huge strides towards our ultimate goal, to put our struggle on to a new trajectory where the unity of our country and the establishment of the 1916 Republic becomes inevitable."
The Mid Ulster representative also said the SDLP's rejection of his party's offer of an election pact was a "serious political mistake".
He added: "It demonstrates a lack of strategic vision on the part of the SDLP leadership and is further evidence that they are out of step with the voters and the grassroots.
"I am calling on them once again to seize the opportunity to send out a clear message of support for progressive politics, the Good Friday Agreement and genuine power sharing and partnership government.
"In my view the conditions have never been better for the republican ideal to take root in Ireland.
"Every day more and more people across the island are endorsing our vision of a better future and a new nation founded on genuine fairness and equality."