Speaking to reporters at a scheduled news conference following opening practice at the Sao Paulo Grand Prix, Vasseur confirmed that he met seven-time champion Lewis Hamilton and Charles Leclerc to discuss their clash and performance in Mexico last Sunday.
"The guidelines are always the same," said Vasseur. "They are two competitors with a fighting spirit for sure, but they need to have respect for each other.
"But mainly, and firstly, they need to respect the brand, the team, the people working at home, the people working on track. I think we are putting a lot of effort on this and the message was clear - and will stay clear."
Hamilton, who started from his first pole for the team, had made clear after the Mexican race that he felt Leclerc had been over-aggressive on the opening lap when they tangled and ran off track, wrecking Ferrari's hopes of victory.
The British driver called for serious discussions and confirmed on Thursday that he remained frustrated and would not stop speaking his mind on the issues.
The drivers had not met since the Mexico event as Leclerc returned to Monaco for the birth of his first child.
Vasseur deflected claims, from Hamilton and others, that Leclerc races harder against his team-mates than others by citing his aggressive pass of four-time champion Max Verstappen of Red Bull in Texas.
"If you have a look at what Charles did in Austin in the first sector, everybody said it was magic," he said. "The line is fine between the two, but he didn't crash into the other car."
Vasseur added: "For sure, in this situation, we failed collectively because we were one and two and we didn't win the race at the end. That means that it's clear that we failed and we have to react.
"But the conclusion of the meeting yesterday (Thursday) evening was a clear reminder that the Ferrari is coming first, is coming first for the brand, for the employees, for the Tifosi, and this we have to keep it in mind."
