Stobart floated a possible bid for Flybe last month but has now confirmed it is not planning to make a formal offer.
The two groups have, however, committed to continuing their close working relationship and franchise agreement.
Flybe share prices had fallen by nearly 25% by 9am on Thursday morning following the announcement overnight.
“Stobart Group and Flybe have been unable to reach an agreement on satisfactory terms,” said Stobart in a statement.
“The board of Stobart Group has determined it is not in shareholders’ best interests to increase its latest proposal for Flybe above the level which was rejected by the board of Flybe.
“Given this, Stobart Group confirms it does not intend to make an offer for Flybe.
“Stobart Group and Flybe enjoy a range of shared interests as well as a growing franchise arrangement between the two groups’ airlines and it is Stobart Group’s intention to continue the collaborative working relationship between both companies.”
A Flybe spokesperson added: “The board of Flybe Group Plc notes the announcement by Stobart Group Limited withdrawing its approach regarding a possible offer for Flybe.
“The board remains highly confident in the prospects of Flybe and believes the group continues to have an exciting future as an independent company, delivering the sustainable business improvement plan set out in June 2017.
“This plan is focused on driving sustainable profit and cash generation and will see the fleet size reduce to an optimum level for the number of identified profitable routes and make the business demand-driven rather than capacity-led.”
Stobart, which owns Southend and Carlisle Lake District airports, last month said it was interested in being part of a cash bid for the regional carrier.
Exeter-based Flybe has an existing franchise agreement with Stobart, Stobart Air, which operates some Flybe services and also flies as Are Lingus Regional.
Flybe issued two profit warnings last year, citing IT issues and maintenance costs, as well as rail competition and weaker winter demand.