Obama led Romney 53 percent to 43 percent in Ohio and had a 53 percent-to-44 percent bulge in Florida, results from the New York Times-Quinnipiac University-CBS News polls indicated.
The three organizations are collaborating on polling in six states.
The polls' results were released on the day Romney wrapped up a three-day bus tour of the Buckeye State and Obama made campaign stops at two university campuses in Ohio.
In Florida, among those who said they "definitely" will vote, 36 percent identified themselves as Democrats, 27 percent said they were Republicans and 33 percent said they were independents.
In Ohio, 51 percent of likely Romney voters said they strongly favor him, while about 66 percent of likely Obama voters said they strongly favor him, results indicated.
Results are based on interviews with 1,196 likely voters in Florida and 1,162 likely voters in Ohio conducted Sept. 18-24. The margin of error for both polls is 3 percentage points.