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.
Republicans around the country have unleashed heavy criticism against President Barak Obama days after he forcefully defended the construction of a $100 million Islamic center two blocks from the site of the 2001 terror attacks.
Many republicans said that while they respect religious freedom, Obama's position lacked compassion and empathy for the victims' families.
Last Friday, Obama said that Muslims "have the same right to practice their religion as everyone else in this country" and that included building the Islamic center in lower Manhattan.
Obama told reporters that his remarks weren't an endorsement of the specifics of the mosque plan.
When inquired about his remarks during a townhall-style meeting in Ohio on Wednesday, the president said he has "no regrets" about what he said.
Locally, California GOP Senate challenger Carly Fiorina said on Tuesday that the mosque should be built at a different location.
Fiorina's opponent, Democratic Sen. Barbara Boxer, said building the mosque is a zoning decision that should be decided locally.
The Islamic leader, Imam Feisal Abdul Rauf, who is behind the plans for the mosque, is taking a three-nation outreach trip to the Middle East promoting religious tolerance. The cost of the trip, roughly $16,000, is being footed by the U.S. government, according to the State Department.
The department said Rauf will get a daily $200 honorarium for the 15-day tour to Bahrain, Qatar and the United Arab Emirates.
Airfare is included, as well as the standard federal government per diem for expenses and lodging in each of the cities he will visit, spokesman P.J. Crowley said. Those per diem rates range from nearly $400 to nearly $500, according to official documents.
State Department officials made it clear that Rauf is expected to discuss Muslim life in America. He is not allowed to raise funds for the planned ground zero mosque while on the trip.
While many are bitterly against the proposed mosque near ground zero, no one has complained about a chapel at the Pentagon where many Muslims have been praying for years - just 80 feet from where another hijacked jetliner struck. The chapel hosts separate weekly worship services for Muslims, Jews, Hindus, Mormons, Protestants, Catholics and Episcopalians. It seats about 100, and 300 to 40 Pentagon employees come to pray each week.
Meantime, American Muslims who support the proposed ground zero mosque and Islamic center are facing skeptics within their own faith who argue that the project is insensitive to Sept. 11 victims and is needlessly provocative - especially at a time when Muslims are pressing for wider acceptance in the U.S.
A professor of Islamic studies at American University likened the project to "rubbing salt in open wounds."
The Associated Press contributed to this report.