Andy Burnham said Tuesday he handled the exchange with a fake Susie Wiles "in the right way" and was not embarrassed by the episode.
The prime minister said "nothing of consequence" was discussed in the messages, framing the incident as a limited security lapse rather than a substantive breach.
POLITICO reported Monday that Burnham had messaged someone posing as Wiles, Donald Trump's chief of staff and a senior White House adviser.
Wiles had previously been targeted in a phone hack, though the White House said that earlier breach was not connected to the impersonation case.