An Australian company owned by Rupert Murdoch’s News Corp has launched its third attempt to buy UK property website Rightmove.

The REA Group of property sites announced on Monday it had upped its offer for Rightmove to £6.1bn.

Earlier efforts to acquire the London Stock Exchange-listed Rightmove had been rejected. One offer valued the company at £5.6bn but was rebuffed as undervaluing the business.

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News Corp, which is still majority-owned by Mr Murdoch, owns UK newspapers The Sun and The Times as well as businesses and publications worldwide like The Wall Street Journal, New York Post, The Australian and publishers Harper Collins.

The continued push to acquire Rightmove signals the conglomerate’s desire to move further into property.

As well as the REA Group, News Corp owns Realtor.com, an online marketplace for buying and renting homes.

Under UK rules governing corporate takeovers, REA had to update the market of a firm intention to bid for Rightmove by 30 September.

The latest offer says current Rightmove shareholders would continue to own 20% of the company.

Rightmove’s share price had another bump and was up 2.7% on the news of the latest bid.

It described the latest offer as an “unsolicited, non-binding and highly conditional proposal”.

Rightmove added it will “carefully consider” the latest bid with its financial advisers.

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In the announcement on Monday morning, REA there had been no “substantive engagement” with Rightmove.

“We are genuinely disappointed at the lack of engagement by Rightmove’s board and we strongly encourage the Rightmove board to engage,” the announcement said.

It added the latest offer “represents a highly compelling proposition for Rightmove’s shareholders at a significant premium to relevant trading metrics”.

“This proposed transaction would bring together two highly complementary digital property businesses for investment and growth,” REA continued.