The Siena College poll showed 63 percent of the state's voters surveyed oppose the project, with 27 percent supporting it. That compares with 64 percent opposed and 28 percent in favor two weeks earlier, results that are within the polls' sampling margins.
Democrats nationwide, including President Barack Obama, have defended the proposal as protected by the Constitution's guarantee of religious freedom. Many Republicans have called it an affront to the memory of those killed in the 2001 attacks at the World Trade Center.
In a new question, the latest poll found that many in the state believe the project is protected by the Constitution, even if they oppose the plan.
Nearly two-thirds of voters, 64 percent, say the developers have a constitutional right to build the mosque. Twenty-eight percent say they do not.
Among those who oppose building the mosque, about half agree that developers have the constitutional right to build it. Twenty-eight percent of mosque opponents say they do not have that right.
The telephone poll questioned 788 registered New York state voters Aug. 9 through Monday. It has a margin of error of 3.5 percentage points.