Sen. Ted Cruz on Thursday defended his decision to challenge the Electoral College certification process, pushing back against some of his colleagues who have accused him of inciting Wednesday's deadly riots at the U.S. Capitol by casting doubt on the 2020 election.

"What I was doing is debating on the floor of the Senate election integrity," Cruz said during an interview with KXAS-TV, an NBC affiliate in Fort Worth, Texas. "That has nothing to do with this criminal terrorist assault, which was wrong and needs to be prosecuted. It's exactly the opposite. What I was doing is how you're supposed to resolve issues in this country." 

Cruz's comments came one day after a rally intended to support President Trump descended into a mob that stormed the Capitol during the certification of the Electoral College vote, forcing lawmakers, staff and reporters to shelter in place in both the House and Senate. One woman was shot and later died, and three other individuals died from "medical emergencies."

Capitol Police officer also died Thursday night after sustaining injuries during the riots.

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Cruz slammed the violence as a "despicable act of terrorism" and "a shocking assault on our democratic system."

In social media posts later removed by Facebook and Twitter, Trump – who has maintained, without evidence, that the election was rigged – told the rioters, "We love you" and "You're very special," but asked them to "stay peaceful" and later to "go home." By Thursday evening, Trump promised there would be an "orderly transition of power" and acknowledged for the first time that a new administration would take over on Jan. 20 when President-elect Joe Biden is inaugurated. 

"A new administration will be inaugurated on Jan. 20," Trump said, after lawmakers called for invoking the 25th Amendment and removing him from office. "My focus now turns to ensuring a smooth, orderly and seamless transition of power. This moment calls for healing and reconciliation." 

Like other lawmakers, Cruz said he believed Trump's rhetoric had contributed to the siege on the Capitol. 

"I do think the president's rhetoric and his language has been over the line. I think it was irresponsible. I think it was reckless. And I think he needs to recognize it," he said. 

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Asked whether he believed Trump needs to be removed from office, Cruz demurred: "We're 13 days out, and he's going to leave at noon on Jan. 20." 

While the majority of Democrats, and some Republicans, blamed Trump for inspiring the siege of the Capitol, others accused Cruz of promoting sedition and lawlessness by repeating the president's baseless rhetoric that the election was rigged.

"Sen. Cruz, you must accept responsibility for how your craven, self-serving actions contributed to the deaths of four people yesterday. And how you fundraised off this riot," Rep. Alexandria Ocasio-Cortez, D-N.Y., tweeted on Thursday. "Both you and Senator Hawley must resign. If you do not, the Senate should move for your expulsion."

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While Cruz did not parrot Trump's unfounded claims about ballot manipulation and fraud, he did emerge as one of the most ardent advocates in the Senate for challenging the certification of Electoral College votes. He led a group of 11 senators demanding a 10-day delay to audit the election results and an emergency investigation, though no evidence of widespread fraud has emerged in the two months since the election. 

Cruz eventually withdrew his objections for Georgia, Michigan and Nevada, but co-signed the opposition to Pennsylvania once the Senate reconvened in the wake of the riot.

Congress formally certified Biden's Electoral College victory early Thursday morning.