British insurer Direct Line Insurance on Wednesday rejected a takeover offer of 3.28 billion pounds ($4.16 billion) from bigger rival Aviva, saying it "substantially undervalued" the company.

On Nov. 19, Aviva made a 250-pence-per-share offer, which represented a nearly 60% premium to the stock's close a day earlier.

If the deal went through, Direct Line shareholders would have received 112.5 pence in cash and 0.282 new Aviva shares for every Direct Line share held.

Separately, the life, motor and home insurer Aviva, said Direct Line has refused to engage in further discussions.

The chairpersons of both companies have spoken directly to explain why Direct Line was rejecting the offer, a person with knowledge of the matter said.

Direct Line said its board considered Aviva's proposal with its advisers and concluded that it was "highly opportunistic".

According to British takeover rules, Aviva has until Dec. 25 to make a firm offer or walk away.

In March, London-based Direct Line also rejected a 239-pence-per-share takeover bid from Belgian rival Ageas , which was 4.6% lower than Aviva's offer.

Shares of the UK insurer have fallen as much as 14% since Ageas abandoned its pursuit in the same month.

However on Thursday, Direct Line shares jumped 36% on the news in early trading, while Aviva shares fell 2.7%.

Direct Line — under the leadership of its new CEO Adam Winslow, who joined the company from Aviva in March — has engaged in efforts to energize a business struggling in a weak motor market.

The company missed expectations for half-year operating profit in September, hurt by its underperforming motor insurance arm.

It has implemented aggressive price hikes to mitigate the rising costs of claims and announced plans to cut 550 roles, or about 5% of its global workforce, earlier in November.

Direct Line said on Wednesday it continues to make progress towards its financial and profitability targets under its turnaround strategy.

(Reporting by Raechel Thankam Job in Bangalore; Additional reporting by Carolyn Cohn and Anousha Sakoui; Editing by Devika Syamnath, Shilpi Majumdar and Shounak Dasgupta)