The second-largest employer of Australian physicians took four days to reject the proposal from its major shareholder to buy the shares it did not already own, saying the approach was "opportunistic and fundamentally undervalues Healius."

But shares of Healius, formerly known as Primary Health Care, held above the price they were trading at before the Chinese construction materials company made its approach, a sign that investors remained hopeful of a more compelling bid.

The shares were down 6 percent at A$2.59 by late afternoon on Monday compared with Jangho's A$3.25 indicative offer price, but still higher than the A$2.25 last closing price before the Chinese firm made its approach.

"These sorts of things are always just opening gambits," said Morgans Stockbroking analyst Scott Power.

"If (Jangho) is serious they'll come back and keep pushing. It's early days in these takeover negotiations."

The Chinese company owns 16 percent of Healius, not enough to block a rival bidder, Power said.

Jangho in a statement said it was "disappointed that the Healius board has so promptly dismissed an offer that represents compelling value for Healius shareholders".

The proposal to buy Australia's second-biggest medical centre operator highlights the interest Chinese investors have in health-related companies, which are seen as high-quality assets with possible use back home, where an ageing population is straining existing services.

That interest has coincided with a difficult stretch for Australian health stocks which have been battered by concerns about tightening government subsidies and soft consumer spending. Hospital operator Healthscope Ltd is also fielding foreign takeover approaches following a decline in its share price.

In 2015, Beijing-headquartered Jangho paid $200 million for Australia's biggest eye care provider, Vision Eye Institute Ltd.

If Jangho did buy Healius, it would be one of the mainland's biggest healthcare plays in Australia. But it would need to clear the cross-border merger-and-acquisitions regulators of both countries.

(Reporting by Byron Kaye in SYDNEY and Aditya Soni in BENGALURU; Editing by Christopher Cushing)

By Byron Kaye