In a statement confirming what sources told Reuters earlier on Tuesday, Atlantia said its board had examined the preliminary offer presented by CDP and investment funds Macquarie and Blackstone.
CDP said late on Monday the consortium aimed to sign a memorandum of understanding with Atlantia by Oct. 28 with a binding offer to follow after 10-weeks of due diligence.
But Atlantia's board decided to give CDP extra time to submit a better offer.
"The board has considered the economic terms and the conditions at this stage as not yet compliant and suitable for ensuring a fair market valuation of its Autostrade stake," the infrastructure group said.
Atlantia said its board would meet again on Oct. 28.
Atlantia has been embroiled in a legal dispute with Rome since 2018, when a bridge run by Autostrade collapsed killing 43 people. The government has threatened to strip it of its motorway licence.
Two sources close to the matter said the offer by the CDP-led consortium could value Autostrade at up to 9.5 billion euros before applying a discount for the risks of future damage claims linked to the bridge collapse and possible changes in the company's tariff system.
Activist fund TCI and Spinecap fund, two minority investors in Atlantia, have said Autostrade could be worth between 11 billion and 12 billion euros.
Last week, CDP and Atlantia began exclusive talks to try to rescue a deal that had foundered over a series of issues including valuation and legal liabilities.
Atlantia needs to secure an offer it deems attractive in the short-term or it will have to fall back on previous plans for a spin-off of its Autostrade stake.
The group has a shareholder meeting scheduled for Oct. 30 and will press ahead with a vote to spin off Autostrade and sell it to institutional investors unless CDP delivers an attractive offer in time, sources have said.
CDP has asked Atlantia to postpone the meeting to give more time for negotiations.
Leading proxy advisers Glass Lewis and Institutional Shareholder Services have recommended Atlantia's shareholders vote in favour of the spin-off of the motorway assets, according to documents seen by Reuters.
(Additional reporting by Giuseppe Fonte in Rome, editing by Jane Merriman, Valentina Za and Tom Brown)
By Stephen Jewkes and Francesca Landini