The owner of the Mulberry fashion brand has rejected an increased £111m bid from Mike Ashley’s Frasers Group to buy the British luxury handbag maker, saying it has “no interest” in selling its shares.

Challice, a group controlled by Singaporean entrepreneur Christina Ong and her husband, Ong Beng Seng, which owns 56% of Mulberry – giving it the power to block any bid – called on Frasers to ditch plans to take over, saying it came at an “inopportune time” for the struggling brand.

The statement came after Frasers Group, which already owns 37% of Mulberry, increased its offer for the rest of the group to 150p a share late on Friday after an earlier £83m bid – worth 130p a share – was rejected by the company earlier this month.

The offer from Frasers, which owns Sports Direct, House of Fraser department stores, Evans Cycles and the Flannels luxury streetwear chain, came after Mulberry said it needed to raise cash after it tumbled to a £34m pre-tax loss in the year to the end of March, after a slide in sales.

Frasers, which lost £150m on the collapse of the Debenhams department store chain where it was a shareholder, said it had made the bid for Mulberry as it would “not accept another Debenhams situation where a perfectly viable business is run into administration”.

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

On Sunday, Challice welcomed Frasers decision to participate in the fundraising round in which the Sports Direct owner bought £3.9m of new Mulberry shares.

However, it said: “Challice has no interest in either selling its Mulberry shares to Frasers or providing Frasers with any irrevocable or other undertaking with regards the possible offer.”

It pointed out that Frasers would be unable to take over Mulberry without its support, and said: “Challice hopes that by making its position clear, Frasers will be encouraged to announce that it does not intend to make an offer for Mulberry.”

It said it was “very supportive of the company and its current management team” and believed in the long-term value of the Mulberry brand.

“Challice believes that it is an inopportune time for Mulberry to be sold and particularly regrets the distraction that the possible offer is bringing to the company and its management team at this time.”

Mulberry – founded in 1971 by the entrepreneur Roger Saul and his mother, Joan, is best known for its leather goods, particularly women’s handbags.

In recent times it has struggled to compete against bigger international brands, especially since the post-Brexit ending of shopping tax breaks for tourists to the UK.

Thierry Andretta, who led Mulberry from 2015, oversaw a push to take it upmarket, but the arrival of Baldo, who previously ran the fashion label Ganni and was involved in a turnaround at the Italian streetwear brand Diesel, is expected to herald a shift back to a broader appeal.