BBC News with Sue Montgomery

Votes have been cast across the United States in a tightly fought presidential election with campaigning continuing even on polling day itself. The Republican candidate Mitt Romney is taking the rare step of campaigning in two battleground states as voting takes place. Speaking to supporters outside Cleveland, Ohio, he said it was critical that as many people go to the polls as possible.

People are making calls to get folks out to vote, because they know we get folks out to vote we'll have the real change, we really needed in this country. And I'm so excited about the prospects. I've got to tell you, I'm buoyed by the spirit of the people across the nation, the enthusiasm, the support, the energy. It is just amazing. Thank you.

By contrast, the Democrat

incumbent

, Barack Obama held his final rally late on Monday. Opinion polls have suggested that Mr Obama has a narrow lead in most of the key states, but the result will be very close.

We feel confident, we've got the votes to win, but it's going to depend ultimately on whether those votes turn out. And so I would encourage everybody on all sides just to make sure that you exercise this precious right that we have and that people fought so hard for us to have.

Special measures have been put in place to

facilitate

voting in large parts of the eastern United States still affected by last week's massive storm, while the majority of polling stations in New York are said to be working normally, some have had to