Sadiq Khan's office said false material was being "circulated and amplified by a far-right group".
A Met spokesperson said specialist officers had reviewed the content.
They described it as "artificial audio" that had been brought to the attention of the force.
Security minister Tom Tugendhat said he was aware of the fake and called for people not to "repost or amplify it".
It came as the Met prepared for anunprecedented security operation ahead of a pro-Palestine demonstrationin London on Armistice Day on Saturday.
The force has warned there is a risk of clashes with far-right groups.
In one piece of fake audio circulating on social media, the words falsely purporting to be those of Mr Khan suggest Remembrance events could be put back a week.
The phoney speech also draws comparison between Remembrance events and the pro-Palestinian demonstration in terms of importance.
The Met is deploying almost 2,000 officers across central London throughout Saturday and Sunday, Armistice Day and Remembrance Sunday respectively.
A spokesperson for the force explained: "Officers from Counter Terrorism Policing continue to review online content and material that is referred to us by members of the public.
"We will investigate and take enforcement actions where criminal offences are identified."
Police say faked audio purporting to capture the Mayor of London calling for Armistice Day to be re-scheduled for a pro-Palestinian march "does not constitute a criminal offence".