At least 20 personnel are members of the Australian Defence League, which is affiliated with the hardline English Defence League, known for its links to football hooliganism and violent street marches.

It is understood some work in the frontline of Australia's efforts to control the number of asylum seekers coming to Australia by boat.

On its Facebook page, the ADL has called for members to go to Lakemba Park for Australia Day. One member wrote: ''It'll be great fun, bring your baseball bats and cricket bats. There will be a lot of balls to hit.''

The page's administrator cautioned members that ''you do understand that if their [sic] is an issue your public comments on here may become a component of an investigation''.

After Fairfax Media provided the Australian Defence Force with screen shots of more than 20 ADL members, who listed their employment as the navy, the army and Defence, a spokeswoman said it would take swift action.

''Navy has initiated an investigation into this matter and as such, it would be inappropriate to make further comment,'' she said. ''Army is currently conducting inquiries into reports that army personnel are associated with the Facebook page.

''Should it be confirmed that any serving member of the ADF has made comments on any Facebook page which are contrary to defence values and social media policy, disciplinary and/or administrative action may be taken.''

The ADF introduced strict social media guidelines for members in January last year, including private use where they could be identified as an employee or member of the ADF.

Last week, Fairfax Media revealed Defence was investigating a navy member who had commented on a friend's Facebook post about asylum seekers.

The friend, who claimed to be an Australian Defence League member, wrote about asylum seekers whose boat had sunk, claiming they had come to Australia ''to jump on Centrelink and get free government housing''.

The navy member commented: ''I'm about to head out today to deal with these f---ers.''

After the post was shared hundreds of times, the navy member closed his Facebook account.

The defence spokeswoman said the ADF would pursue disciplinary action against any member who broke its social media policy, including its anti-discrimination rules.

A spokeswoman for Customs and Border Protection said: ''Officers are aware of their responsibilities under current policies detailing the responsible use of online social networks [and] employees who breach this policy will be dealt with in accordance with this internal policy and the [Australian Public Service] values and code of conduct.''