Concerned Citizens of Canberra, a small group described by a judge as having a "generalised hostility to the Muslim religion", managed to stymie the mosque's construction for years on planning grounds.

Similar groups have sprung up to oppose mosque developments across the country, including in Bendigo, and, more recently, in South Hurstville in Sydney.

The 500-capacity mosque to be built on The Valley Avenue in Gungahlin was approved by the ACT's planning authority in 2012.

Soon after, the Concerned Citizens group launched court action against the decision to approve the mosque's development, and against the planning authority's decision not to extend its consultation period.

Their case was based mainly on a string of planning objections, including that there would be insufficient parking, traffic congestion, and excessive noise.

Concerned Citizens also argued the planning authority's decision-making process was defective, and raised concerns about the use of the mosque as a "funeral parlour".

The group was dealt a major blow when then ACT Supreme Court Master David Mossop found it had insufficient standing, or wasn't directly enough affected, to mount the challenge in July 2014.

After that decision, its Christian fundamentalist leader, Irwin Ross, bizarrely linked the development to the kidnapping of Nigerian schoolgirls and the Boston Marathon bombing.

The group then lodged a late appeal against Master Mossop's decision, but Justice Richard Refshauge found they had no reasonable prospects for success.

In dismissing their attempted appeal, Justice Refshauge described the group's interest in the development as no more than that of an "intermeddler or busybody".

That left just one avenue of appeal open to the group: the High Court.

Concerned Citizens was still considering such a move late last year.

But Mr Ross confirmed on Friday the group would not pursue the matter legally any further.

He said the decision by Justice Refshauge left Concerned Citizens with no real prospect of success.

Mr Ross said the decision was not influenced by financial considerations.

"We felt it was a public interest thing, which a lot of people would say it is, so it's more that the judge has said certain things in his decision, so it's sort of made it cut and dry on us," he said.

"But we've felt all along that they haven't really given us a good chance to say things.

"With the judge not being with us on the matter much, we felt that if it's going to some more judges, they would take that into serious consideration."

The construction of the mosque is continuing, and Mr Ross said his group would "monitor" its progress, and watch "all the other things" that are happening around the country too.

"We'll monitor how the mosque is going, because we feel it's of a public concern," he said.

In his judgment against the group, Justice Refshauge said Mr Ross appeared to have a "generalised hostility to the Muslim religion and concern about what he saw as its spread".

The group was comprised of five people, most of whom did not live near the Gungahlin site.

It attempted to boost its membership ahead of the court case, which required the group to show it was directly affected by the development.

Well after the court action began, Mr Ross told his fellow Concerned Citizens that the group "urgently need[s] more members, especially in the Gungahlin region".

Mr Ross lived 10km away from the mosque site.

The group boosted its membership to 18 by the time it reached the ACT Supreme Court.