Alexander suggested that stronger gun control laws are needed following the Aurora, CO mass shooting at a Dark Knight Rises screening. The incident left 12 dead and more than 50 injured.
The Seinfeld star tweeted in the hours after the attack: "I cannot understand support for legality of the kind of weapon in this massacre. It's a military weapon. Why should it be in non-mil[itary] hands?"
He later wrote a follow-up post where he revealed that his stance on guns garnered a harsh reaction from many.
"There have been many tweets of agreement and sympathy but many, many more that have been challenging at the least, hostile and vitriolic at the worst," Alexander wrote. "Clearly, the angry, threatened and threatening, hostile comments are coming from gun owners and gun advocates."
Alexander's statement continued: "Despite these massacres recurring and despite the 100,000 Americans that die every year due to domestic gun violence - these people see no value to even considering some kind of control as to what kinds of weapons are put in civilian hands."
The actor also invited those who disagree with his comments to simply boycott his work.
He concluded: "This is not the time for reasonable people, on both sides of this issue, to be silent. We owe it to the people whose lives were ended and ruined… to insist on a real discussion and hopefully on some real action.
"In conclusion, whoever you are and wherever you stand on this issue, I hope you have the joy of family with you today. Hold onto them and love them as best you can. Tell them what they mean to you. Yesterday, a whole bunch of them went to the movies and tonight their families are without them. Every day is precious. Every life is precious."
Alexander's full statement can be read here.
The alleged Aurora, CO shooter James Holmes appeared in court for the first time on Monday (July 23), although he has yet to be formally charged. He will return to court next Monday (July 30).
Aurora's district attorney has said that a decision on pursuing the death penalty against Holmes could be delayed for up to 60 days.
Watch footage of James Holmes in court below: