Philip Morris is competing with a US private equity firm to buy the asthma medicine company Vectura.
Carlyle said it would not increase its £958m ($1.33bn) bid for drugmaker Vectura after Philip Morris had increased its offer to more than £1bn.
The private equity firm said earlier it considered its final offer of £1.55 a share as “full and fair”.
Vectura makes inhaled medicines and devices to treat respiratory illnesses.
The firm counts Novartis and GSK among its customers.
The takeover of the Vectura had been due to enter a rare head-to-head auction process, after the regulator, the Takeover Panel, gave the two bidders a week to make their best offers for the FTSE 250 firm.