Projections give Mr Bush 254 Electoral College votes and Senator Kerry 252.
The votes are too close to call in three states, including Ohio.
In Iowa, problems with vote-counting machines in two small counties will delay results for at least one day.
New Mexico is also undeclared for either candidate.
Early projections put turnout at more than 115 million voters -10 million more than in 2000.
As well as electing a president, Americans are also choosing members of Congress and some state governors.