With the LaLiga title race heating up between rivals Madrid and Barcelona, the duo have exchanged views publicly, mostly about refereeing decisions.
But Ramos wants to put that behind them on international duty, with Spain preparing to face Israel in a World Cup qualifier before a friendly against France.
"It's the way it is between Real Madrid and Barcelona and that will not change," he told a news conference on Monday, via AS.
"Now, I will give him a hug. We have become accustomed to throwing stones, but we take it without malice and it is always healthy.
"That serves as something for you to sell. The key is the unity in the team, and that cannot be lost."
Ramos' Madrid are two points clear of Pique's Barcelona atop LaLiga, the former having delivered at the opposite end to which is expected.
The 30-year-old has scored 10 goals in all competitions this season – the first time he has reached double figures in his career.
"I didn't expect to score as many goals. It is the best record of my career as a goalscorer, but I don't think too much about it," Ramos said.
"As a defender, I am thinking more about conceding as little as possible. If I can score in important matches late on, even better."