Tight Ohio race
McCain could successfully clinch the Republican nomination if he succeeds in wresting Texas and Rhode Island from Huckabee, the former Arkansas governor.
|Clinton says she is determined to stay|
in the race [EPA]
Polls in Rhode Island close at 0200G, while Texas polls close at 0200G, although the state also holds Democratic caucuses after the primary vote.
NBC news has reported that the Democratic primary race in Ohio remains too close to call despite earlier polls indicating that Clinton held a slight lead.
Exit polls conducted by AP in Ohio showed Clinton enjoying strong support among her core voters, such as whites, union members and less affluent voters.
Obama, meanwhile, was winning nearly all the black vote as well as capturing younger and wealthier voters, AP said.
Al Jazeera's Kimberly Halkett, reporting from Ohio, said turnout was considerable with more than 50 per cent of the state voting.
Some polling stations were being kept open because of poor weather, she added.
The two Democratic contenders were also said to be running neck and neck in Texas.
Al Jazeera's Rob Reynolds, reporting from Texas, said that turnout had been enormous, with queues outside polling stations.
A big question in the state remained whether Clinton would successfully capture the Latino vote - one quarter of Texas's population - while the state's cities of Houston and Dallas have sizeable African-American populations which Obama hopes to win, Reynolds said.
Both Democratic candidates had campaigned fiercely in Ohio and Texas, with Clinton continuing to criticise Obama over his perceived lack of experience during campaign stops in the two states.
|Both Democratic candidates campaigned |
hard ahead of Tuesday's vote [GALLO/Getty]
Obama swiftly countered that he had a sizeable delegate lead which "is going to be hard to overcome", and casting doubt that Clinton's campaign could "blow us out of the water in Ohio and Texas".
Bill Clinton, the former US president and Hillary's husband, has said that his wife must win both states to realistically continue her bid to capture the White House.
Clinton, however, has remained upbeat, saying she was still "really optimistic" on Tuesday while outside a school in Houston, Texas.
She has also refused to speculate on her next move should the polls not favour her campaign.
"We are going to get through today, and we are going to see how we do," she said.
"I believe in taking things one day at a time in politics, as in life."