Hamilton said that the 20-year-old Verstappen’s youth and inexperience were harming Red Bull’s chances.
But with the two set to race again this weekend in the Chinese Grand Prix, the 33-year-old Hamilton said he approached Verstappen in Shanghai in a bid to defuse the tension.
“Being that I am the older driver I thought it important that I went to him,” the four-time world champion said.
“So I just shook his hand and said I’m sorry about the last race. Regardless if it is his fault or my fault, it doesn’t really matter. It’s in the past,” he added.
“Hopefully that sign of respect… helps you kind of turn the page and move forward.”
It wasn’t clear how Verstappen reacted to the apology.
But the Dutch driver, whose aggressive style has made him a fan favourite on the Formula One tour, earlier told reporters he won’t change how he operates.
Asked why he thinks Hamilton took aim at him, Verstappen said: “Why? Because it’s quite simple and easy to blame the younger driver.”
“That’s the only way I can see it. But like I said, you know, these things happen. There’s no reason for me to change anything.”
Verstappen and Hamilton collided early in the race in Bahrain, forcing the Dutchman to retire and the Briton to settle for third, just behind his Mercedes teammate Valtteri Bottas.
The race was won by Sebastian Vettel for Ferrari, giving him two straight victories after also taking the season-opener in Australia.
Hamilton has blamed Verstappen for what he called a “silly” and “unnecessary collision”, while Verstappen has insisted Hamilton was at fault.
On Thursday, Hamilton praised Verstappen’s ability.
“I have a lot of respect for Max and he’s got great potential to be a champion. He’s such a talented driver,” he said.
“Still, it’s such a learning process with all the pressure being in a top team, and you’re constantly learning… So he’s going to have some great rides and he’s going to have some bad races, just as I will.”
“But I think respect needs to be kept between all the drivers.”
Hamilton is going for a record sixth Chinese Grand Prix win this week with Mercedes aiming to bounce back after Ferrari’s two consecutive victories.