A majority of people in 11 Republican-voting states believe he is performing poorly, according to polls carried out by Gallup since the President's inauguration.
Less than half of people in 33 states nationwide think he is doing a good job, the research found.
Those include Texas and Indiana, where Mr Trump comfortably beat Hillary Clinton in November's election, as well as states where he achieved slimmer margins of victory, such as Arizona and North Carolina.
He was given a 40 per cent average approval rating by the 81,000 Americans polled by Gallup between his inauguration and June 30.
The President's worst rating was 26 per cent in Vermont, followed by 29 per cent in Massachusetts. Six in 10 people surveyed in West Virginia and 59 per cent in North Dakota said he was doing a good job, his best ratings.
Mr Trump polled 46 per cent of the nationwide vote in the 2016 election, winning in 30 states.
His first six months in the White House have been dogged by controversies, including allegations of Russian meddling in the election. He has also struggled to push through key policy pledges, such as the repeal of ObamaCare.
He later insisted the 36 per cent rating was "not bad at this time", while also claiming the survey was "just about the most inaccurate poll".