Piers Morgan has defended his "right to be allowed to have an opinion"
Some 57,000 complaints have been made about the show's coverage of the Oprah Winfrey interview on 8 and 9 March.
On 9 March, Morgan said he "didn't believe" a word Meghan had said. He left the ITV programme later that day.
The total of 57,121 complaints is 12,600 more than those made over a race row on Celebrity Big Brother in 2007.
The duchess herself is among those who have complained to the watchdog.
Morgan responded on Twitter: "Only 57,000? I've had more people than that come up & congratulate me in the street for what I said. The vast majority of Britons are right behind me."
Ofcom, which has regulated British TV since 2003, has already launched an investigation into Good Morning Britain. On Wednesday, a spokeswoman said the investigation was ongoing.
A further 4,398 complaints have been made about the Oprah interview itself, which was broadcast on ITV on 8 March. Some objected to the duke and duchess' claims about the Royal Family, some about the timing given the Duke of Edinburgh's ill health, and some about the use of allegedly misleading press headlines in the programme.
Ofcom said: "We're assessing the complaints against our broadcasting rules, before deciding whether or not to investigate." The regulator did not say which aspect of the interview had attracted the complaints.
In the in-depth interview, Meghan told Oprah her mental health became so bad she "didn't want to be alive any more", that she did not receive the help she asked for from Buckingham Palace, and that an unnamed member of the Royal Family had queried "how dark" their son Archie's skin might be.
The day after its UK broadcast, Morgan said he did not believe her, adding that "the fact that she's fired up this onslaught against our Royal Family I think is contemptible".
He briefly walked off the programme after clashing with weather presenter Alex Beresford, and he was criticised by mental health charity Mind.
Morgan later conceded that it was "not for me to question if she felt suicidal", but has defended his "right to be allowed to have an opinion".
Do you know great minds enjoy excellence, average minds love mediocrity and small minds adore comfort zones?