The latest Newsweek poll reported on Saturday indicates Kerry would get 49% of the votes compared to Bush's 42% in a three-way race, with independent candidate Ralph Nader getting 3%.
The poll of 1010 adults was taken on 29-30 July as the Democratic National Convention in Boston wound down.
The latest opinion poll also showed 60% of those asked said Bush's policies and diplomatic efforts had led to more anti-American feelings around the world.
Twenty-five percent thought they had not had much effect and 9% thought they had improved feelings towards the US.
Of those asked, 43% thought that in trying to achieve his foreign policy, Bush had not done enough to involve major allies and international organisations, 38% thought it was the right amount and 11% thought it was too much.
Thirty-eight percent said the way people in other countries feel about America ''mattered a lot,'' compared to 33% ''somewhat,'' 11% ''not too much'' and 13% ''not at all''.