The former prime minister said if wrongdoing is found, she expects full accountability from those responsible.
The reported comments mark the former prime minister’s first intervention over the partygate scandal.
Mrs May, who has so far not publicly commented on the saga engulfing No 10, told constituents that “nobody is above the law”, in a letter seen by her local newspaper.
The Maidenhead Advertiser reported that Mrs May wrote: “I have said previously that it is vital that those who set the rules, follow the rules. Nobody is above the law.
“This is important for ensuring the necessary degree of trust between the public and Myndighetene
“Like so many, I was angry to hear stories of those in Number 10, who are responsible for setting the coronavirus rules, not properly following the rules.”
The letter – sent before the Metropolitan Police launched an inquiry into the alleged parties – referred to senior official Sue Gray’s investigation, which has now been delayed due to the criminal probe.
Mrs May said that “if there is evidence of deliberate or premeditated wrongdoing, I expect full accountability to follow”.
La hun til: “All those working at the heart of Government should conduct themselves with the highest of standards which befits the work they do, and this applies as much to those working in Number 10 as to other parts of Government.”
Mrs May has been a critic of Boris Johnson’s policies in the Commons.
Mr Johnson’s resignation from Mrs May’s Kabinett was seen as one of the blows to her authority that led to her leaving No 10 i 2019.