The Curia question was whether respondents agreed or disagreed that: "If an adult wishes to use a drug such as marijuana, they should be able to do so legally."
Only 38 per cent of men and 28 per cent of women agreed, while 57 per cent of men and 63 per cent of women disagreed.
Agreement peaked at 42 per cent in the 18-40 age group but fell to 30 per cent among those aged 41-60 and 23 per cent in the 60-plus age group.
Both Labour and especially National voters opposed legalisation, but it gained a bare majority of 50 per cent among those supporting other parties, where only 40 per cent disagreed with it.
In contrast, the UMR poll of 1000 members of the agency's online panel asked: "Which of the following is closest to your views on the marijuana laws?" The options were: "It should remain illegal and anyone caught using it should get a criminal record," "It should remain illegal but be decriminalised - anyone caught using it would get fined but would not get a criminal record," and "It should be legalised."
UMR research director Gavin White said the result was virtually the same as UMR's previous poll using the same question in 2011, and Mr McCoskrie obtained a different result only by leaving out the decriminalisation option.
"He's being mischievous as hell since the debate is not about legalisation. From what I'm picking, it's about decriminalisation," he said.
He said the online panel was chosen using "strict quotas" to ensure that it matched the population on key demographic variables.
Who supports legalising cannabis
* 38 per cent of men
* 28 per cent of women
* 42 per cent of 18-40 years
* 30 per cent of 41-60 years
* 23 per cent of 60-plus years
* 25 per cent of National voters
* 40 per cent of Labour voters
* 50 per cent of other voters
* 33 per cent of all adults
Source: Curia Research