The latest figure represents a decline from 33 per cent in March, according to the CNN-SSRS polling. Approval among Republicans has also fallen, from 73 per cent in March to 60 per cent in the latest survey.
The findings come as the conflict approaches its seventh month. CNN reporting says Trump had previously suggested that the fighting could last only days or weeks, but the conflict has continued for several months.
The poll also indicates that views about the conflict are not uniform among Republicans. Although 60 per cent of Republicans approve of Trump's handling of the war, that figure is lower than earlier in the conflict, showing a decline in support within his own party.
A separate Reuters/Ipsos poll conducted in September found that 34 per cent of Americans approved of US strikes on Iran, while Trump's overall job approval stood at 32 per cent. The survey questioned 1,277 US adults and had a margin of error of three percentage points.
The two polls measure different things and should not be treated as identical. The CNN-SSRS survey focuses specifically on Trump's handling of the Iran war, while the Reuters/Ipsos survey separately measures views of US strikes against Iran and Trump's overall job performance.
The polling comes as Trump prepares to address the United Nations General Assembly in New York, where the Iran conflict is expected to be among the international issues discussed. CNN reports that the White House expects Trump to reiterate its position that Iran must not be allowed to obtain a nuclear weapon.
The war is also becoming part of the domestic political debate in the United States, particularly as the November midterm elections approach. Reuters has reported that Republican Senate candidates in Michigan and Iowa have called for a faster end to the conflict, differing from Trump's position.
The latest polling does not establish whether the United States is objectively winning or losing the war. The question measures Americans' perceptions of the conflict rather than providing an independent military assessment.
Similarly, responses about whether Trump is doing enough to end the war reflect the views of people surveyed at the time of the poll and do not determine the eventual course or outcome of the conflict.
For now, the latest CNN-SSRS figures show that 26 per cent of Americans approve of Trump's handling of the Iran war, while Republican approval stands at 60 per cent, down from 73 per cent in March. The Reuters/Ipsos survey separately found 34 per cent support for US strikes on Iran and an overall presidential approval rating of 32 per cent.
