'Big battle' ahead
McCain's victory comes one month after his success in multiple states on so-called "Super Tuesday" gave him a large lead in the delegate race and led to his main rival, former Massachusetts governor Mitt Romney, dropping out.
At a speech in Dallas, Texas, McCain looked ahead to the presidential election and said "the big battle is to come".
"I do not underestimate the significance nor the size of the challenge," he said.
"I understand the responsibilities I incur with this nomination and I will not ... slight a single one."
He is expected to be formally endorsed by George Bush, the US president, later in the week.
His former rival, Mike Huckabee, also speaking in Texas, announced he was dropping out of the race and said he had spoken with McCain to congratulate him.
He also urged the Republican party to unite behind one candidate.
"It's now important that we turn our attention not to what could have been or what we wanted to have been but what now must be, and that is a united party," the former Arkansas governor told supporters.
Al Jazeera's correspondent Rob Reynolds in Dallas, Texas, said that the task ahead for McCain was to work out how to bridge the gap with the Republican party's social conservatives, who still viewed him with suspicion.
|Clinton says she is determined to stay|
in the race [EPA]
On the Democratic side, Barack Obama won the state of Vermont, his 12th victory over Democratic rival Hillary Clinton, but Clinton won in Rhode Island, NBC projected.
The races in the Ohio and Texas, which hold high numbers of delegates, remained too close to call, although some early projections showed Clinton held the lead in Ohio, which has 141 delegates, and Obama narrowly ahead in Texas - which has 193.
Clinton's campaign on Tuesday accused Obama's supporters of engaging in "outrageous" and "undemocratic" tactics in Texas, such as locking her supporters out of caucuses, charges dismissed by the Obama campaign as "laughable", AFP reported.
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 kept open later because of poor weather, she added.
|Both Democratic candidates campaigned |
hard ahead of Tuesday's vote[GALLO/GETTY]
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.
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."