The president leads Mr Romney among likely voters by a margin of three percentage points in Virginia and two percentage points in Ohio and Florida, Ipsos's online tracker found.
None of the polls indicates a clear lead for President Obama because each falls within the survey's credibility interval, a tool used to account for statistical variation in online polls.
The two candidates are tied in Colorado, the tracking poll showed. Nationwide, they are tied at 46% each. Neither candidate has held a clear lead in the four-day national tracking poll since early October.
Collectively, the state polls indicate Mr Obama holds a slight advantage in the state- by-state battle to rack up the 270 electoral votes needed for a victory.
Some 52% of voters say they expect Mr Obama to emerge the victor in the election, while 32% say they think Mr Romney will win.
Mr Obama holds his greatest advantage in Virginia, a state that was considered reliably Republican until the 2008 election. He leads Mr Romney by 48% to 45% there, just within the poll's credibility margin of 3.4 percentage points.
Mr Romney yesterday made his closing pitch to the American people, warning undecided voters that four more years of Barack Obama risked plunging the US into another recession.
Hours after monthly job figures showed the US economy added 171,000 jobs last month, but unemployment rose fractionally to 7.9% – the highest rate since Franklin Roosevelt was president – Mr Romney urged voters to consider the president's record in office, not his words.
"Look beyond the speeches, the attacks and the ads, and look to the record, to the accomplishments and the failures and the judgments. Words are cheap, a record is real," he told a crowd in West Allis, Wisconsin.
He added: "Today's increase in the unemployment rate is a sad reminder that the economy is at a virtual standstill. The jobless rate is higher than it was when President Obama took office, and there are still 23 million Americans struggling for work."
Meanwhile, the president also savagely attacked a Romney campaign advert that falsely suggested Jeep was moving production to China, accusing his opponent of stretching the truth to scare voters in the final days of the campaign. He said: "This isn't a game. These are people's jobs. These are people's lives."
While running through the positives of the latest unemployment figures, Mr Obama added: "We have made real progress, but we are here today because we know we've got more to do. Our fight goes on because this nation can't succeed without a thriving middle class."
The unemployment rate edged up slightly because the number of people looking for jobs increased. These were people who had previously given up hope of finding work, but who now think they may have a better chance.
The total workforce, which is the number of people either working or looking for jobs, rose by 578,000 in October.
Meanwhile, it emerged the total number of political adverts aired during the election season has passed the one million mark, a 40% increase over the 2008 and 2004 elections.