In his explanation for leaving Sunday's game, Mr Pence stressed that he stood with Mr Trump on the issue.
Pence left the game after some players knelt during the National Anthem, saying he did not want to "dignify" the demonstration.
Hillyard also tweeted that Pence's staff offered no further details about the phone call Trump claims to have had with Pence before the game.
Donald Trump's war on the NFL took a new turn last week, when his campaign exploited the national anthem to fundraise for his re-election bid and legal fees. So he made sure his administration was consistent with their position on Sunday.
He had previously tweeted a photograph of himself at a Colts game, adding he was "looking forward to cheering for our Colts".
Pence tweeted about his departure and reiterated his support for President Donald Trump's combative stance on the kneeling protests, which swept the National Football League last month.
NBC's Vaughn Hillyard reported from Indianapolis that the media pool was kept in vans ahead of the game instead of being led inside with Pence.
Although many liberals lauded the NFL players for defying Trump and politicizing the national anthem, the sport's loyal fan base hasn't offered such resounding levels of support, as ratings plummeted.
So the vice president shouldn't be shocked that the game he attended featured a protest during the anthem.
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