One of the Prime Minister's media advisers has resigned after admitting they told someone about Tony Abbott's presence near the Tent Embassy in Canberra on Thursday.

The furious protest that caught up Julia Gillard and the Opposition Leader was sparked when an activist at the Tent Embassy told protesters Mr Abbott was at a function only a few hundred metres away.

They were incensed by remarks made by Mr Abbott earlier in the day in which he said he thought it was probably time to reconsider the relevance of the Tent Embassy.

A commercial radio station yesterday morning reported that a member of Ms Gillard's staff had tipped off the protesters.

The Prime Minister's office says that did not happen although a media adviser - named as Tony Hodges - did call another person and told them Mr Abbott's whereabouts.

Former media adviser Tony Hodges ( supplied )

A spokesman for Ms Gillard says the information was then passed on to a member of the Tent Embassy.

The spokesman says the staff member did not in any way encourage violence or demonstration but that it was an error of judgment and has resigned.

On Thursday, Ms Gillard and Mr Abbott had to flee an awards ceremony at a Canberra restaurant when it was surrounded by about 200 protesters who had been marking the 40th anniversary of the establishment of the Embassy.

Dozens of police were called to hold off the protesters who were banging on the glass walls of the restaurant, shouting "shame" and "racist".

Police hustled both leaders to the Prime Minister's car, with Ms Gillard stumbling and losing a shoe as she was dragged to safety.

The Opposition has called for an inquiry into the circumstances surrounding the adviser's resignation.

"The Prime Minister should immediately initiate an Australian Federal Police inquiry into who the schedule was released to, and for what purpose, and into whoever was involved in the decision to breach the Leader of Opposition's security," Liberal frontbencher Christopher Pyne said.

"The Opposition finds it remarkable that the staffer would have acted unilaterally and we believe the Prime Minister needs to do more than simply scapegoat one staffer."

March on Parliament

On Friday, more than 200 activists marched from the Tent Embassy to Parliament House in Canberra, chanting outside the front doors, "always was, always will be Aboriginal land".

Some protesters then burnt an Australian flag to loud cheers. Watch here

On the way to Parliament House, the demonstrators blocked Commonwealth Avenue, one of the city's main thoroughfares.

After about an hour, the group marched back down the hill.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Listen Duration: 4 minutes 41 seconds 4 m 41 s Aboriginal protesters burn flag at Parliament ( Samantha Donovan ) Download 2.1 MB

Children were among those who burnt the flag, including this girl, who spoke to reporters.

"I don't want my kids to grow up and not have parents. I don't want my kids to be taken away from me when I'm older," she said.

"I'm heaps angry with the flag and the Government; it's stupid."

There was a strong police presence at the protest.

One of Aboriginal leader at Thursday's protest says many of the protesters in front of Parliament were severely embarrassed by the flag burning and wanted to distance themselves from it.

The elder, who did not want to be identified, told PM that: "We're not going to get respect if people are burning flags."

'Move on'

The group went to Parliament House as tensions remained high after the dramatic scenes two days earlier.

Yesterday morning Tent Embassy spokesman Mark McMurtrie told ABC News Breakfast that it was Mr Abbott's comments and his proximity to the Tent Embassy that triggered Thursday's protest.

"He made the comments in an inciteful and smug manner in Sydney and then flies several hundred kilometres to come down and sit 100 metres from us," he said.

While Mr Abbott praised the Prime Minister and her security team for getting them both out of a "difficult situation", he repeated his remarks about the Tent Embassy and said they were "perfectly reasonable".

"I think the sense of grievance which motivated the establishment of the Tent Embassy all those years back ought not to be as intense today and that's why I said it was time to move on," he said.

Meanwhile, members of the Tent Embassy have returned Ms Gillard's missing shoe after it had earlier been put up for auction on eBay.