"This never happened," The Sun quoted a Kensington Palace spokesman as saying, in response to the argument claims.
The source had also told The Sun, "It's a tricky situation but it was a one-off and they are determined to maintain a positive relationship even though they are obviously very different in their approach."
The two sisters-in-law have rarely been seen together in public since the May 19 wedding.
The Sun further reported that Meghan left Kate "in tears" over her demands for Princess Charlotte's bridesmaid dress after an allegedly "stressful meeting."
Royal aides neither denied nor confirmed the incident.
Rumors of a feud between Kate and Meghan were fuelled after Kensington Palace announced last month that the Duke and Duchess of Sussex would move out the palace complex, where they and the Duke and Duchess of Cambridge reside in separate units, and relocate to Frogmore Cottage at Windsor Castle "as they prepare for the arrival of their first child."
