Mr Adams said republican ambitions for Irish unity had been boosted by the decision to hold a referendum on Scottish independence in two years. "This is a live issue at this time and has been given added impetus by the recent decision to hold a referendum in 2014 on Scottish independence," he said.
"The Good Friday Agreement provides for a border poll on Irish unity. Sinn Fein, in the new year, will commence a campaign to achieve this. That means we need to build momentum and support so that the Irish and British governments are persuaded to hold a border poll.
"We will then have to campaign for a 'yes' vote and to persuade the people of the island of Ireland to support unity and the creation of a new Republic."
Under the terms of the 1998 Good Friday Agreement the Secretary of State can call a border poll if a mood change is detected. However, it can only be called once every seven years. In his address to an audience in New York, Mr Adams said Sinn Fein would have to persuade people on both sides of the border of the benefits of unification.
He also urged Irish Americans to use their influence, adding: "Irish America needs to persuade political opinion in America that a united Ireland is in the best strategic interests of the USA. And we need Irish America to support the holding of a border poll."
In March 1973 the question of Northern Ireland's continued participation in the UK versus a united Ireland was raised with the sovereignty referendum. The result was an overwhelming vote in favour of remaining within the UK.
DUP MP Nigel Dodds said unionists were not concerned about the likelihood of a new border poll being held. He said: "Even if by some miracle Gerry Adams were able to persuade Americans that the future of Cork is of greater strategic interest to the USA than the future of Chicago or even China, the decision on a border poll would not actually be affected.
"A border poll can only be called by the Secretary of State when there is likely to be a vote in favour of changing our constitutional status. The DUP is not concerned about the likelihood of such a poll being held, nor are we worried about what the outcome would be. All recent evidence actually points to a strengthening of support for the maintenance of Northern Ireland's position within the UK.
"The only people who cling to the notion of a border poll are Sinn Fein and a few gullible commentators who claim it would somehow bring stability. The reality is that in Northern Ireland as in the United States the issues of importance to our citizens are the stability of our economy and the prospects for employment."