SYDNEY--EQT AB's pursuit of Perpetual looks over after the Australian investment manager rejected its US$2.6 billion takeover proposal and said it had stopped engaging with the Swedish private-equity provider.

Perpetual on Monday said EQT-controlled Windflower had proposed an all-cash payment of 22.50 Australian dollars a share, equivalent to US$16.03.

The price matched Windflower's second indicative offer, but this time Windflower said it would pay the full amount even if Perpetual declared a December-half dividend of up to A$0.60 a share in the interim.

Perpetual said its board still believed the proposal undervalued the company, and flagged several assumptions by Windflower that it said raised unacceptable risks over whether the transaction would succeed.

"As the further revised proposal was expressed as a best and final proposal (in the absence of a competing proposal), Perpetual considers that the process of engagement with EQT has now concluded," Perpetual said.

In July, Perpetual said it had received a proposal valued at A$21.64 a share from Windflower. It increased that to A$22.07 and then to A$22.50 the same month, prompting Perpetual to provide limited nonexclusive access to its books in hopes of attracting an acceptable offer.

EQT is already working to expand its portfolio of Australian assets, which includes cancer-care provider Icon Group and one of the country's best-known rugby league franchises.

In August, Cleanaway Waste Management accepted a proposal by EQT that valued its equity at close to US$5 billion. Last week, Cleanaway said EQT was continuing its due diligence and remained committed to entering an implementation deed.