In Arizona, Florida, Michigan, North Carolina, Pennsylvania and Wisconsin – all of which Trump won in 2016 – Biden has the edge.
However, it shows the race as still being hotly contested, with the result hanging in the balance.
Wisconsin is the safest of the six, with Biden leading by 53 per cent and Trump claiming 45 per cent of support.
North Carolina is the narrowest of the six, with Biden generating a wafer-thin 49 per cent of support, and 47 per cent backing Trump.
Across all six the average is 50 per cent for Biden, and 46 per cent for Trump.
Voters are pictured standing in line to cast their votes in North Carolina on October 15
In Florida, 51 per cent of respondents said they were voting for Biden, versus 48 per cent for Trump; in Arizona, 50 per cent backed Biden, and 47 per cent Trump.
In Michigan, Biden was winning the support of 51 per cent of voters, while Trump had 44 per cent.
And in Pennsylvania, where a fight over the counting of ballots went all the way to the Supreme Court, Biden won 50 per cent, versus 46 per cent for Trump.
The swing-state poll surveyed 3,328 people from Thursday to Sunday and has a margin of error of plus or minus 1.7 pe