The British handbag maker Mulberry has rejected an £83m takeover proposal from Mike Ashley’s Frasers Group as too low, insisting instead that it would push on with a planned fundraising to support a turnaround.

The luxury brand said it had considered the approach carefully and consulted its 56.1% majority shareholder Challice, controlled by the Singaporean entrepreneur Christina Ong, who had “no interest” in pursuing the possible offer.

Frasers, which owns Sports Direct, Evans Cycles, the House of Fraser department stores and multiple other retail brands from Slazenger to Jack Wills, has a 36.8% stake in Mulberry. On Monday, it said it was making an offer for the rest of the company worth 130p a share, pitting itself against its rival large shareholder.

The Mulberry board said on Tuesday it believed the recent appointment of Andrea Baldo as chief executive, along with the emergency £10.75m share placing announced late on Friday, “provides the company with a solid platform to execute a turnaround”.

“In light of this, the board has concluded that the possible offer does not recognise the company’s substantial future potential value. In addition, the board has been informed that Challice is supportive of the company’s strategy.”

Frasers has been given a “put up or shut up” deadline of 5pm on 28 October to announce a firm intention to make an offer for Mulberry, or walk away.

Mulberry shares closed at 124p on Monday after hitting a low of 102p earlier in the day.

Monday’s offer from Frasers came after Mulberry had said on Friday that it needed to raise cash after it tumbled to a £34m pre-tax loss in the year to the end of March, from a £13m profit the previous year, with sales down 4% to £153m. It added that sales fell by 18% for the 25 weeks since the period ended.

The brand said on Tuesday it had no intention of withdrawing the fundraising, and it would engage further with Frasers, a “committed and important investor in Mulberry” which had publicly stated that it would be willing to underwrite the placing.

Baldo, who joined on 1 September, previously ran the fashion label Ganni, and was involved in a turnaround at the Italian streetwear brand Diesel. He took over from Thierry Andretta, who had led Mulberry since 2015 and oversaw a push to take it upmarket.

Mulberry – founded in 1971 by the entrepreneur Roger Saul and his mother, Joan, and best known for its leather goods, particularly women’s handbags – has struggled to carve out a place in the luxury market amid heavy competition and the post-Brexit ending of shopping tax breaks for tourists to the UK.