According to AP, the Holy See has issued a statement to the country's ambassador saying that Francis "absolutely did not intend to hurt the feelings of the Mexican people".
It also said Francis in no way wanted to detract from Mexico's efforts to combat drug trafficking.
Francis' comment was made in an email the pontiff wrote to an Argentinian friend, Gustavo Vera, who heads an NGO called 'Alameda' which is involved in combating organised crime and human trafficking.
"I hope we [in Argentina] can avoid Mexicanisation", wrote the pontiff.
"I have spoken with Mexican bishops and it is a terrifying reality", he added in the message, which Vera then made public.
On Tuesday, Mexico's foreign ministry voiced its "sadness and concern" at comments which it said "stigmatised" the country, in a diplomatic note to the Holy See.
