Mr Pence spoke at a news conference on Wednesday afternoon outside the First Baptist Church of Sutherland Springs, where the shootings happened.
He said the gunman lied on his background check application when buying the weapons. He also cited the man's history of mental illness and bureaucratic failings within the Air Force for the tragedy.
Mr Pence began his trip to Texas by visiting Brooke Army Medical Centre at Fort Sam Houston in San Antonio to meet with victims wounded in the shooting.
Then he, his wife and Texas officials met with victims' families, first-responders and two men who pursued the gunman.
Mr Pence said President Donald Trump had authorised a full complement of federal resources to the investigation, including 100 on-site FBI agents.
