Australia's richest person, mining magnate Gina Rinehart, reportedly took her stake in press group Fairfax to 12.8 percent Wednesday, prompting government calls for tougher media ownership laws.

The iron ore billionaire acquired close to 8.0 percent of the group after launching a Aus$200 million ($212 million) share raid late Tuesday, bringing her total holding to about 12.8 percent, Dow Jones Newswires said.

Rinehart had been seeking a further 9.9 percent stake in the newspaper, radio and digital media firm in which she already held more than 4.0 percent to become its largest shareholder, the Australian Financial Review said.

Communications Minister Stephen Conroy said Rinehart, who has been critical of the Labor government's mining tax on iron ore and coal profits, was seeking to exert her influence but her actions were within the law.

Laws designed to diversify media ownership prevent Rinehart from taking more than 15 percent of shares in the respected company which publishes The Sydney Morning Herald, Melbourne paper The Age as well as the Financial Review.

"Do we need stronger laws in this area? Yes," said Conroy.

"We want to see a debate around a public interest test.

"But governments cannot pass laws on the basis of who they like and dislike and whose views they like and dislike."

A government-commissioned review of media ownership laws in the digital era has already made a draft recommendation that major media takeovers be subject to a yet-to-be-defined public interest test to ensure a diversity of views.

Conroy said Rinehart would not be the first rich Australian to become a major media player in a country where Rupert Murdoch and the late Kerry Packer have held significant assets.

"All that's really changing is that a different wealthy individual is taking a strategic or ownership position in some media," he said.

"What we have to ensure is that we have diversity of opinion and ownership. The current parliament needs to examine what we need to do to strengthen those laws."

Shares in Fairfax soared on the development, gaining 10 percent to close at 81.50 cents.

The Australian Financial Review said a broker believed to be acting for Rinehart had Tuesday offered 81.8 cents a share for Fairfax after the market closed -- a more than 10 percent premium on its close of 74 cents.

Mining heiress Rinehart made a splash when she entered the media sector in late 2010, taking stakes in commercial television station Ten Network and Fairfax.

Rinehart's fortune stems from her late father's iron ore firm which she took over in 1992 and which she is credited with expanding as she developed mines in Western Australia and Queensland.

Her wealth is estimated to have more than doubled to Aus$10.3 billion in 2011 and is expected to keep rocketing upwards as the potential of the vast underdeveloped iron ore and coal deposits she owns are realised.

Fairfax, which dominates Australian media alongside Murdoch's News Ltd, owns websites, newspapers and radio stations.