Presidential elections: A call for presidential elections to be conducted across the 32 counties was unanimously backed at the ardfheis.
The party has published a paper on Irish unity and started a campaign for the Government to publish a Green Paper, setting a deadline of a year.
Delegates also backed a call that all post offices in Northern Ireland should offer the Irish passport postal processing scheme. Thirty-five so far provide the service.
An Omagh party member told the conference that former GAA All-Ireland champions, Tyrone, could lift the Sam Maguire cup but could not vote in a presidential election.
Another delegate, Daniel Daly from Belfast, said voting rights should not be limited to "just the six counties. People north of the Border "must be granted full citizenship rights now", he said.
During a 20-minute session on the "all-Ireland agenda" chief party negotiator Martin McGuinness claimed that in the negotiations last December, the DUP "signed up for the all-Ireland agenda set out in the Good Friday agreement and began a constructive engagement with the Irish Government and with nationalist opinion for the first time.
"I welcome these tentative but significant first steps," he added.
Mr McGuinness stressed the need for ongoing consultation and negotiation on Irish unity. He said that economic institutions operated on an all-Ireland basis and "the imperative of Irish unity is clear from an economic and social perspective". He said: "We must continue to engage unionists in a way that allows them to feel comfortable and to participate in this debate on their own terms."
