The Mexican, second in a championship already won by Verstappen for the third year running, emphasised the slogan of a local #racepect campaign in saying what happened on track must stay on track.
"I think it's important that we give this message because I think media likes to create these sort of driver rivalries outside the track," he told reporters at the Autodromo Hermanos Rodriguez on Thursday.
"We are a great sport, a great example for a lot of young generations and we should just be focused on the sport side.
"Whatever happens on track should always stay there and that's the best message we as a country want to give to the rest of the world."
Verstappen has won 15 of 18 races so far this season, wrapping up his third drivers' title in Japan last month, while Perez has lost his way.
Although he has a contract for 2024 there has been continued speculation about his future with Red Bull and what might happen if he fails to secure second place in the championship.
The Dutchman was booed after winning in Texas last weekend, with many in the crowd supporting Perez or Mercedes' seven times world champion Lewis Hamilton, Verstappen's big title foe in 2021.
With Red Bull concerned about his security in Mexico, the World Champion has been provided with two bodyguards, but told reporters separately that he had no problems so far.
"I am just here to do my job and so far the welcome that I’ve got has been amazing," he said.
Verstappen has won four of the last five Mexican Grands Prix while the country is still waiting for its first home winner. Perez has so far managed no better than third.
Red Bull's Austrian motorsport consultant Helmut Marko riled Mexicans earlier in the year when he blamed Perez's patchy form on his ethnicity and referred to the driver as South American.
Mexican Grand Prix organisers condemned the comments at the time and called for "a more respectful and united Formula One community, encouraging healthy competition both on and off the track."
Verstappen added: "Of course, it’s always good to support your favourite driver but to have respect for others... while being on the podium when the national anthem is being sung or played.
"It's quite disrespectful when you start chanting through these moments so that’s why I think it’s good they’re raising awareness."
