"I went to Esteban's room and had a talk with him," Perez told an Italian Grand Prix news conference at which Ferrari's championship leader Sebastian Vettel sat between the two drivers.
Perez, who said the conversation had been "really good", added that they had agreed to forget the past and push on with the interests of the Silverstone-based team.
"We cannot afford to lose any more points ... we will move forward and I'm very sure that these things will not happen again," the Mexican said.
"A new relationship starts from now on. I really hope that from now on we can be working as a team."
Force India are fourth in the constructors' championship but collisions between their drivers have cost them plenty of points already this season.
They clashed twice at Spa, with Ocon squeezed towards the wall as he tried to pass Perez in the second incident that most upset the 20-year-old and led to a Twitter outburst against the Mexican.
Ocon posted a clip of the incident on Sunday evening and told his 64,000 followers: "Perez tried to kill me 2 times!"
The collision was the latest in a build-up of bad blood, with the drivers warned in June about their conduct after they collided at the Azerbaijan Grand Prix with podium places up for grabs.
Force India principal and co-owner Vijay Mallya has said he will now "implement a policy of team orders" to prevent more such incidents.
"I think we both crossed the line, that's for sure," said Ocon, agreeing that they needed to put the team first.
"I think also we need to get the bosses' trust back and maybe after some races they will let us race again," added the Frenchman, who confirmed he would follow any instructions issued by the team.
Perez, 27, said both were experienced enough to know how to handle the situation.
"Esteban has been racing for a long time as well ... there will be some instructions coming up for us. I think we will put everything in place that the interests of the team come first, before us," he said.
(Reporting by Alan Baldwin; Editing by Alison Williams)
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