LONDON (Reuters) - Stobart Group has scrapped plans to buy Flybe Group, it said on Thursday, adding the UK-based regional airline had rejected a bid and it had decided against making a higher offer.

Stobart, an infrastructure and support services company, said in February that it was considering bidding for Flybe as part of a consortium.

Flybe has been hit by faltering demand and the company's shares lost almost a third of their value in 2017.

"The board of Stobart Group has determined that it is not in its shareholders' best interests to increase its latest proposal for Flybe above the level which was rejected by the board of Flybe," Stobart said in its statement.

Stobart shares were unchanged while Flybe shares were down almost 24 percent to 35.5 pence as of 0814 GMT.

Flybe said in response to Stobart withdrawing its approach: "The board remains highly confident in the prospects of Flybe and believes that the group continues to have an exciting future as an independent company."

It plans to cut costs by reducing its fleet.

Stobart said it would continue to work with Flybe as the two operate a franchise agreement between their airlines. Its aviation arm operates some European flights for Flybe from London Southend Airport, which Stobart owns.

Stobart started life as haulage business Eddie Stobart but has switched its focus away from lorries in recent years.

Trucking firm Eddie Stobart Logistics, best-known in Britain for its distinctive green and red lorries, is now separately listed on the London stock market.

(Reporting by Sarah Young; editing by Kate Holton and Jason Neely)