Sir Stelios Haji-Ioannou and family have agreed to support Apollo's cash acquisition of easyJet, pledging their entire stake and taking the unlisted share alternative.
Castlelake confirmed it will not make an offer for easyJet, ending speculation triggered by their joint approach statement last month.
EasyJet has extended Castlelake's takeover deadline to Friday, matching Apollo's and setting up a decisive week in the two-way bidding war for the budget airline.
"Pricing has been attractive, driving strong late booking demand for our flights and holidays," said chief executive Kenton Jarvis.
The Takeover Panel has extended the put-up-or-shut-up deadline after Castlelake offered a "best endeavours" regulatory commitment on its fifth takeover proposal for the airline.
easyJet's board has unanimously rejected a fourth acquisition proposal from Castlelake, citing undervaluation and concerns over deliverability, while granting the bidder nine additional days to submit a higher offer.
Private equity firm Castlelake said it is in the early stages of considering a possible offer for easyJet, and the carrier's board said it has had no approach while reserving the right to consider any proposal.
Castlelake said it is in the early stages of considering a possible offer for easyJet without having approached the company's board.
The low-cost airline said the result was in line with its April trading statement and flagged that the Middle East conflict has raised fuel costs and reduced forward visibility for H2.