Adams spoke to hundreds of Irish-Americans filling a large ballroom at a Manhattan hotel, The Irish Times reported.
"With your support, we have made progress," he said. "There is an end to armed conflict ... and I believe the political and economic dynamics in Ireland today make a united Ireland a realizable and realistic objective in a reasonable period of time."
Irish nationalists will have to reach out to unionists, the majority in Northern Ireland who want to maintain ties to Britain, Adams said, and engage in "a patient process of nation-building to unite orange and green."
Britain partitioned Ireland in the early 1920s, when the Catholic-majority south gained independence. In the 1960s, a violent unionist response to a Catholic civil rights movement led to 30 years of sectarian killing.
Adams told the Times in an interview before he addressed the conference that Sinn Fein does not want a "32-county version of the 26 counties," that a united Ireland should be a new entity.