Forty-seven percent of registered voters nationwide who lean towards a candidate back Romney, while 46 percent support the president. Four percent are undecided. The 1 percentage point difference is within the survey’s three-point margin of error.

Romney leads by eight points among men; the president leads by five points among women.

The president’s supporters are more likely to strongly back their candidate. Fifty-two percent strongly favor Mr. Obama, while just 29 percent of Romney voters strongly back the presumptive Republican nominee.