The poll gave Obama the support of 49 percent of those surveyed. Romney got 40 percent. That's up from a 45-41 percent split last month.
Fox noted it is Obama's biggest lead since Romney became the presumptive GOP nominee.
Fox said the president is gaining traction among independents as he seeks a second term. While Romney had held the advantage among independents through early June, Obama now holds an 11 percentage-point edge with 30 percent of independents saying they still haven't made up their minds, Fox News said.
The Fox News Poll, conducted jointly by Anderson Robbins Research and Shaw & Co. Research, surveyed about 930 registered voters by phone Sunday through Tuesday. The margin of error was 3 percentage points.