The Barcelona centre-back has been the subject of jeers from Spain fans during national team training sessions in recent days in the wake of his support for the Catalan independence referendum last Sunday.
There has also been speculation of a falling-out with Real Madrid captain Ramos after a tweet from Pique in support of the controversial vote provoked further anger among some supporters.
Pique held a news conference on Wednesday where he insisted he is fully committed to the national team's cause and would not be forced into retirement by his critics.
The 30-year-old stressed he has an excellent relationship with Ramos and is even planning on a future business venture with the former Sevilla man.
"It's a lie that I get on badly with him," he said. "We will be partners in a business I proposed.
"My relationship with him is phenomenal. I'd like you to see that."
Pique again refused to state whether he is in favour of Catalonia seceding from Spain but has urged politicians to hold positive dialogue after the dreadful scenes last Sunday, when voters clashed violently with police after the Spanish government declared the referendum illegal.
"It's the million-dollar question and I'm not going to answer it," he said when asked if he supported a split. "Footballers are global figures and I can't put myself on one side or the other. I'd lose half of my followers from Catalonia or Spain.
"My sons, for example, are Colombian, Lebanese, Catalan and Spanish. We're a global world."
He continued: "The relationship between Spain and Catalonia is like a father and an 18-year-old son who wants to leave home.
"Spain has two options: to talk like a father should, or to see the son leave. It's difficult to understand what's happening in Catalonia without being there.
"What does it matter what I think? What matters is that politicians do their job and find a solution."