He said: "I think it's going to be close. I don't think anybody really knows exactly what's going to happen."
With a combined 187 delegates, Indiana and North Carolina are the two biggest primary contests left in the Democratic voting calendar in the run-up to the party's national convention in August.
Clinton boosted her campaign for the nomination when she won the Pennsylvania primary on April 22.
While Obama has sought to distance himself from controversial remarks made by his former pastor, support for Clinton in North Carolina has grown, eroding Obama's lead in that state.
The New York senator is also leading Obama 49 per cent to 43 per cent in Indiana, according to a Suffolk poll with a margin of error of plus or minus four percentage points.
Al Jazeera's Rob Reynolds, reporting from Indiana, said: "These primaries allow a chance for Senator Hillary Clinton - perhaps her last chance - to turn this race around.
"In order to do that, she must win here, in Indiana, and either win or come very close to winning in North Carolina."
Clinton has argued that she is the Democrats' best hope of winning the White House, in part because she is more popular with the party's working-class base.
Reynolds said: "For Barack Obama this is an opportunity to gage how much, if at all, he has been damaged by the re-emergence of his controversial former pastor ... and also to overcome the impression that his campaign has hit some rough patches."
The candidates clashed a day earlier over Clinton's plan to suspend the federal vehicle fuel tax, with Obama saying that his rival's proposal to suspend the levy over a holiday period was a "stunt".
But in a campaign advertisement aired on Monday, Obama said that Clinton was offering "more of the same old negative politics".
Clinton's advertisement claimed she is "the candidate who is going to fight for working people".
As per Democratic party rules, delegates up for grabs on Tuesday are shared out according to the proportion of the vote received by each nominee.
Each nominee requires 2,025 delegates to secure the nomination to run for the US presidency.
|Democrats are concerned about a protracted |
battle between Clinton and Obama [AFP]
With neither candidate likely to reach 2,025 delegates by the final primary vote in June, the contest is likely to be decided by superdelegates – high-ranking Democrats that can vote for their preferred nominee regardless of primary and caucus results.
From contests held so far, Obama holds 1,746 pledged delegates to Clinton's 1,611, according to MSNBC figures, including superdelegates who have already pledged their allegiance to the candidate of their choice.
After Tuesday, only six state contests will remain.
The 16-month battle between Clinton and Obama has raised concerns in the Democratic party that it will appear disunited to voters ahead of the November general elections.