Obama leads Romney 47 percent to 44 percent in combined polling from Florida, North Carolina, Ohio and Virginia.
The poll has a 4.5 percent margin of error.
Obama will need to win about half of the electoral votes provided by Florida, Michigan, North Carolina, Virginia, Colorado, Nevada, New Mexico, Iowa, Ohio, Pennsylvania, Wisconsin and New Hampshire, if he is to secure a second term.
According to a USA Today/Gallup poll released earlier this week, Obama now leads in those states by an average of 9 percentage points, largely because of an 18 percent advantage among women voters.
Obama also leads Romney by 4.5 percent nationally, according to the Real Clear Politics average of polls.
On Friday, the president’s approval rating hit the 50 percent mark for the first time since last June, according to Gallup’s daily tracking poll.