Sir Bernard Hogan-Howe would only express regret for the torment suffered by the former defence chief and his late wife while 22 detectives searched their house last year.
The D-Day veteran was interviewed under caution and kept under suspicion for 10 months until being cleared in January.
The investigation – part of controversial Operation Midland – has been described as one of the most shameful episodes in the Met’s history.
The Metropolitan Police Commissioner told the Home Affairs Select Committee: “We don’t only apologise to people because they’re famous. We apologise where there’s good cause.”
During one terse exchange, Tory MP Tim Loughton referred to a “media circus” surrounding the case.
Sir Bernard, who last week apologised to the widow of Lord Brittan following a shambolic inquiry into a 1967 rape allegation, said: “If what you mean is that you want me to be bullied into apologising then that won’t happen.”