"I left today's Colts game because President Trump and I will not dignify any event that disrespects our soldiers, our Flag, or our National Anthem," Pence said in a statement issued by the White House.
President Donald Trump has criticized players sharply for the protests and pressed the NFL to ban them.
The right to participate in such a protest is protected by the US Constitution's First Amendment.
Critics of players kneeling at the pre-game playing of the national anthem, including Trump, object to any protest, regardless of its merits, during a ceremony meant to honor the US flag and military veterans.
Pence, who has gone out of his way to demonstrate loyalty to Trump, said in his statement it was important to rally around the flag and things that unite the country.
"While everyone is entitled to their own opinions, I don't think it's too much to ask NFL players to respect the Flag and our National Anthem," Pence said. "I stand with President Trump, I stand with our soldiers, and I will always stand for our Flag and our National Anthem."
(Reporting by Doina Chiacu and Jeff Mason; editing by Grant McCool)
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