The Barcelona defender has been vocal about his stance in favour of Catalan independence and praised the voters from Sunday's referendum, which was marred by police violence.
During Monday's training session ahead of Spain's World Cup qualifiers against Albania and Israel, fans hurled abuse at Pique, urging him to quit the national team.
The 30-year-old recently admitted that he would walk away from international duty if his views became a problem for the Spanish Football Federation, but during his pre-match press conference, the defender insisted that his commitment should not be questioned.
"I want to talk, to solve this problem," Pique told reporters. "Being insulted is not nice but it is a challenge for me, I aim to turn this around. Many people across Spain want talks and dialogue.
"I've been coming here since a 15-year-old and here this is like a family for me. You cannot doubt my commitment to the national side. It hurts me that you doubt my commitment. I am proud to be in the national team and be part of this group.
"I've considered retiring as it would be easier for my teammates, but that would be a victory for those whistling. There are many more who oppose their actions than those who carry them out, I am sure of it.
"I don't want to go out of the national team through the back door - the easy route. This team and the federation are my family. I want to continue for them."
Pique has won 91 international caps.