Barkat made the statements in Atlanta during his address to the annual conference of the Jewish National Fund, a nonprofit organization that specializes in the development of Israeli land and infrastructure.
"We just have to say a simple 'No' about Jerusalem to the Palestinians and move on," Barkat said, to loud applause from the crowd of several hundred gathered in a hotel ballroom.
East Jerusalem, the traditionally Arab sector of the city, was captured by Israel in the 1967 Mideast war and annexed. Israel considers the area an integral part of its capital. It is home to important religious sites for Jews, Muslims and Christians.
The international community has never recognized the annexation of the sector, where the Palestinians hope to found the capital of a future independent state.
"Jerusalem must stay a united undivided capital of Israel," Barkat said forcefully, getting a standing ovation. "Jerusalem will not be able to fulfill its goal if, God forbid, it is divided."
Barkat said he has told the current American administration that Jerusalem should be taken off the negotiating table in talks between Israelis and Palestinians.
"There is not one good example in the world of a split city that ever worked," he said.
The United States, which launched a new round of peace talks in Washington last month, says the status of Jerusalem can only be decided in negotiations.
Religious freedom in the city is better than it has ever been, he said, for all residents - Jewish, Christian and Muslim.
Barkat discussed his vision for the future of Jerusalem, focusing mostly on the need to attract more tourists and more business investment. Jerusalem has become the poorest city in Israel, he said, with people leaving, insufficient infrastructure and a shortage of land for development.
His plan for future development would include expansion of both Jewish and Arab neighborhoods based on the city's current population, about two-thirds Jewish and one-third Arab, he said.