Tensions rose when Pique claimed that he was watching a "comedy film" when Arbeloa's Real Madrid were awarded a late penalty against Elche last month, which brought a response from the right-back.
However, Pique has insisted that there are "no hard feelings or bad blood" between the two players ahead of Spain's World Cup qualifier against Georgia on Tuesday.
"I'm not sorry about the Twitter post, but I think it's all been blown out of proportion a bit," Pique told La Vanguardia.
"I made a comment on a situation, I was answered by a Real Madrid player and suddenly there's talk of a big conflict when I didn't send the message specifically to him and Alvaro didn't send the message specifically to me. There are no hard feelings or bad blood between us."
Pique is a slight injury doubt for the Georgia clash.