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Miller, 34, spoke as a federal judge in Dallas, Texas, detained him without bail after the US attorney for the Northern District of Texas labelled him a danger to the community and a flight risk.
“I was in Washington DC on 6 January 2021, because I believed I was following the instructions of former President Trump and he was my president and the commander-in-chief. His statements also had me believing the election was stolen from him,” said Mr Miller in a statement.
“Nevertheless, I fully recognize Joe Biden is now the President of the United States and that the election is over.
“Donald Trump is no longer president and I would not have any reason to continue to follow his lead.
“While I never intended to harm Congresswoman Ocasio-Cortez nor harm any members of the Capitol police force, I recognize that my social media posts were completely inappropriate.
“They were made at a time when Donald Trump had me believing that an American election was stolen.”
Miller is one of dozens of pro-Trump rioters who attacked the Capitol after the twice-impeached president’s “Stop the Steal” rally on 6 January.
““I want to publicly apologize to Congresswoman Ocasio-Cortez and the Capitol police officers,” he added.
“I have always supported law enforcement and I am ashamed by my comments.”
Miller added that he was not armed during the riot and returned to Texas “immediately” after Mr Trump suggested his supporters leave.
The Texas man is charged in US District Court in Washington DC with knowingly entering or remaining in any restricted buildings or grounds without lawful authority; violent entry and disorderly conduct on Capitol grounds; obstructing or impeding any official proceeding; certain acts during civil disorder, and threats in interstate commerce.