Direct Line has rejected a £3.3bn takeover offer from its bigger UK rival Aviva, the second time it has rebuffed a suitor this year.

Aviva, the UK’s largest insurer, said it offered 250p a share, made up of cash and Aviva shares, in a non-binding proposal on 19 November. This was rejected by Direct Line on Wednesday, which has declined to engage further with Aviva.

The announcement came after markets shut. Aviva’s share price closed 1.6% higher at 489.5p, while Direct Line shares slipped by 0.2% to 158.7p. Its share price has fallen by 14% this year, giving the company a market value of £2.1bn. By contrast, Aviva’s shares are nearly 13% higher, valuing it at £13.2bn.

“Aviva believes that an acquisition of Direct Line would be consistent with its strategy to accelerate growth in its UK businesses and further pivot the group towards capital-light business lines,” the insurer said.

It added that it would create a more efficient platform from which to serve existing and new customers, and would allow Direct Line customers to “benefit from Aviva’s breadth, scale and financial strength”.

It stressed that the deal would deliver “attractive returns for both Aviva and Direct Line shareholders”, in the hope that Direct Line investors will put pressure on the board to hold talks with Aviva.

Aviva believes the acquisition would deliver “material cost and capital” benefits, on top of Direct Line’s £100m cost saving programme.

However, Direct Line, known for its motor insurance, said it had considered the proposal with its advisers and concluded that it was “highly opportunistic and substantially undervalued the company”.

It added: “The board has considerable conviction in the capabilities of our newly established leadership team and stands firmly behind their delivery of our strategy. Under this strategy, the company continues to make early progress towards our financial targets, and expects to deliver attractive growth in profitability, capital generation and shareholder returns.”

The Kent-based company said earlier this month that it plans to cut 550 jobs as part of a turnaround plan aimed at saving £50m next year. It lost nearly 400,000 car insurance customers in the past year. Adam Winslow joined as chief executive in March from Aviva, where he ran the general insurance business in the UK and Ireland.

In February and March, Direct Line rejected two takeover approaches from Belgian insurer Ageas, the second valuing it at £3.2bn, at 239p a share, saying it was “uncertain and unattractive” for shareholders. The UK insurer was spun out of Royal Bank of Scotland in 2012 and listed on the London Stock Exchange two years later.

Aviva has sold businesses in France, Italy, Asia and elsewhere to focus on the UK, Ireland and Canada under chief executive Amanda Blanc. In March, it announced it was returning to the Lloyd’s insurance market through the £242m purchase of Probitas and completed the deal in July.

Under UK takeover rules, Aviva has until 5pm on 25 December to announce a firm intention to make an offer or walk away.