The request came at a meeting attended by UNP and SLFP ministers to discuss the prevailing crisis.
The UNP ministers alleged the two officials were trying to create a division between the president and prime minister Ranil Wickremesinghe, and have become an obstacle to the continuation of the government.
They also asked that the Army intelligence chief be removed.
However, the president has made no favourable response to any of the demands.
During the Rajapaksa regime, Lakthilake sided with Wickremesinghe when there was an internal opposition to his UNP leadership, and later campaigned to get Sajith Premadasa appointed the party leader.
He is a one-time UNP organizer for Kotte and member of the Western provincial council.
Bopage, a coordinating officer of Basil Rajapaksa and head of several institutions during the previous administration, supported president Sirisena in his campaign bid.