While the Museum of Australian Democracy heritage manager Edwina Jans has an idea when the message may have been left, she has put out the call for help.

"We think it is from the '80s, potentially 1985, but this is what we want people to tell us, because it references the NDP which we think is the Nuclear Disarmament Party, and the band called the Violent Femmes, and there's one of those anarchy symbols," Ms Jans said.

"I don't know what the connection is - it may have just been a kind of random thing ... 1985 was also when the [anti-nuclear Greenpeace flagship] Rainbow Warrior was bombed, and there was a lot of stuff around nuclear disarmament and peace at that time."

The Nuclear Disarmament Party was formed in 1984 and won more than 640,000 votes in that year's election. It had one successful Senate candidate, who resigned from the party soon after, and a second in 1987. frontman Peter Garrett also stood as a NDP Senate candidate in 1984 - he won 9.7 per cent of the NSW vote but preferences stopped him from being elected.

Violent Femmes, who still tour, formed in Milwaukee as an "acoustic punk band" in 1981 and were a leading alternative act of the 1980s. They sold more than nine million albums. In 2010 Femmes bass guitarist Brian Ritchie joined three former Midnight Oil members (not including the then-minister Garrett) to form surf rock band The Break.

Ms Jans, head of the museum's heritage and collections team, said the message - despite including seemingly random statements and a one-word obscenity - appeared to be political.

"We're really intrigued: the who, the how, the why - because graffiting Parliament House would have been, even in 1985, a pretty audacious undertaking," she said.

"[Like] the activists who painted 'no war' on the Sydney Opera House, what is it about words in a public place - they have enormous power."

Anyone with information on the graffiti - now covered - should email the museum at info@moadoph.gov.au