The two are effectively tied in Florida, Ohio and Pennsylvania, according to a poll conducted by Quinnipiac University, in figures that will provide a boost to Mr Trump’s maverick campaign.
Previous nationwide polls have shown him trailing Mrs Clinton, often by significant margins.
“Six months from election day, the presidential races between Hillary Clinton and Donald Trump in the three most crucial states, Florida, Ohio and Pennsylvania, are too close to call,” said Peter A. Brown, the Quinnipiac Poll’s assistant director.
“At this juncture, Trump is doing better in Pennsylvania than the GOP nominees in 2008 and 2012. And the two candidates are about where their party predecessors were at this point in Ohio and Florida.”
The most encouraging sign for the presumptive Republican nominee was in the midwest state of Ohio, where he led Mrs Clinton by 43 per cent to 39 among registered voters. The same poll showed Bernie Sanders, Mrs Clinton’s opponent in the Democratic race, leading Mr Trump by 43 to 41 points.
Mr Sanders also did better than Mrs Clinton in a head-to-head match-up against Mr Trump in Florida and Pennsylvania – a trend that has also been reflected in many nationwide surveys – but is unlikely to win the Democratic nomination.
Mrs Clinton leads Mr Trump by 43 points to 42 in both Florida and Pennsylvania.
The polls showed support for the two split along gender, ethnic and age lines. Clinton was heavily favoured by women and non-white voters, and those in the 18-34 age range. Mr Trump had significant leads among male, white and 65-and-older voters.
Independent voters, who are not aligned to either the Democrats or Republican, tended to be evenly split between the pair, who both registered negative favourability ratings.
Mr Trump registered higher ratings than Mrs Clinton on questions over honesty and trustworthiness.
No candidate since 1960 has won a presidential election without winning at least two of the states. Barack Obama won all three in his successful 2008 and 2012 presidential election campaigns,
More than 1,000 voters in each state were interviewed for the surveys between April 27 and May 8, partially covering the period when Mr Trump wrapped up the Republican nomination by winning last Tuesday’s Indiana primary.