Easyjet founder Sir Stelios Haji-Ioannou has said he is setting up a new airline called Fastjet.
The move comes as Sir Stelios has been in a number of disputes with Easyjet, in which he and his family own 38% of the shares.
Easyjet said it had a number of rights under its agreement with Sir Stelios and his Easygroup company.
It added that if any Fastjet activity infringed these rights, it would "take necessary action".
Easyjet said it would be seeking "constructive dialogue" with Easygroup and Sir Stelios.
Sir Stelios, who stepped down from Easyjet's board last year, has waged a long-running campaign against the airline's expansion plans.
He has also campaigned for cash to be returned to shareholders.
A month ago, he called for Easyjet to hold an extraordinary meeting to consider the removal of non-executive director Rigas Doganis from the board.
This was a result of Sir Stelios' opposition to the airline's decision to buy new planes from Airbus.
However, last Friday Easyjet said Sir Stelios had withdrawn the extraordinary meeting request.
This was a day after Easyjet announced that it would be returning about £190m to shareholders, including a special dividend worth £150m.