Mr Wallace misspelled a tweet that Mississippi should “succeed from the union” in response to a Twitter thread from a fellow state representative, according to the Washington Post.
Robert Foster had called for all “legal votes” to be counted before a winner in the presidential race was declared.
Mr Biden has already been projected the winner of the White House after achieving 270 electoral college votes.
“Not sure who all needs to hear this but we are not a Democracy. We are a Constitutional Republic,” tweeted Mr Foster.
“The majority does not rule, the law derived from a Constitution has the final say.
“Democrats and their Fake News Cheerleaders are about to get a hard lesson in civics.”
Mr Foster said that Democrats would not accept “the rule of law if it doesn’t end in their favour.”
Mr Wallace then responded in a tweet that has now been deleted: “We need to succeed from the union and form our own country.”
The politician’s account has now been made private.
In a statement to the Washington Post Mr Wallace apologised for the “inappropriate” comment and said, “it in no way represents the desire of my constituents and myself.”