"Here, we make policy. And the tools of our trade are our words and ideas," de Leon, D-Los Angeles, said at the start of Monday's Senate session. "As such, we should always err on the side of more free speech and not less. So last Thursday we failed to keep faith with this historical standard."
Every senator has a right to speak in on behalf of his or her constituents, de Leon said.
Nguyen, a Republican from Orange County, initially said she was swayed by the support she received from fellow senators, saying the public discussion Monday "reaffirms my faith in America's deep belief in the democratic process of freedom of speech."
But about two hours later, her office sent a statement saying Democrats have failed to acknowledge wrongdoing.
"Their continued attempts to mischaracterize this incident as a result of a lack of understanding of the rules is a quick jump to judgment and wrong," Nguyen's statement said. "I hope that never again, a sitting senator will go through the trauma of being forcibly removed from the Senate floor."
Nguyen lived in South Vietnam as a child and fled with her family after its U.S.-backed government fell. Her Senate district includes the largest concentration of Vietnamese people outside of Vietnam. Many fled South Vietnam and blame the U.S. anti-war movement for undermining American forces and contributing to the victory by the communist North.
Senate Minority Leader Jean Fuller, R-Bakersfield, called for a public investigation of the incident and an apology.
Democrats said Nguyen was silenced because she violated Senate rules and would have been allowed to make her speech if she'd waited until later in the session and made the appropriate motion.
Several sergeants-at-arms surrounded Nguyen and gently nudged her toward the door. Nguyen dodged them and continued yelling passages from her speech for nearly a minute as the presiding Democrat, Sen. Ricardo Lara of Bell Gardens, repeatedly told her to stop. Lara was absent from Monday's session.
De Leon stopped short of offering a public apology demanded by Republicans. His spokesman, Anthony Reyes, said de Leon apologized personally to Nguyen following the incident last week.
Hayden was a student radical in the 1960s and helped organize protests against the war. He later became a legislator and elder statesman of the country's left. He died in October, and the Senate held a celebratory memorial for him two days before Nguyen offered her rebuke.
The incident has become a rallying cry for Republican lawmakers and activists, many of whom said it was an example of liberals shutting down speakers with whom they disagree.
Delegates to the GOP state convention over the weekend wore pins with Nguyen's photo.
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AP writer Sophia Bollag contributed to this report.

Updated 6:13 pm, Monday, February 27, 2017