The 17 states, all of which supported the outgoing president, have now filed an amicus brief in support of the case to throw out Mr Biden’s wins in those four states.
Mr Paxton claims that the Covid-related changes to election procedures in the states violated federal law, and he wants the US Supreme Court to block those states in the electoral college.
It is the latest legal effort by supporters of the outgoing president to try and help him cling to power.
But lawyers and backers of the president have suffered a long string of defeats in courtrooms across the country in their attempts to deny Mr Biden his legal victory.
The amicus brief was led by Missouri, according to reports.
Other states whose attorney generals signed on include Alabama, Arkansas, Florida, Indiana, Kansas, Louisiana, Mississippi, Montana, Nebraska, North Dakota, Oklahoma, South Carolina, South Dakota, Tennessee, Utah, and West Virginia.
In his lawsuit filed to the Supreme Court on Tuesday, Mr Paxton claimed that the four states broke the law by changing their election policies and allowed voter fraud to take place.
He also asked the country’s highest court to push back the 14 December deadline for states to appoint their presidential electors.
“That deadline, however, should not cement a potentially illegitimate election result in the middle of this storm,” wrote lawyers for Texas.
Georgia’s Republican Secretary of State Brad Raffensperger has rejected the claim.
"The allegations in the lawsuit are false and irresponsible," said Georgia's deputy secretary of state, Jordan Fuchs.
"Texas alleges that there are 80,000 forged signatures on absentee ballots in Georgia, but they don’t bring forward a single person who this happened to. That’s because it didn’t happen.”
Michigan Attorney General Dana Nessel dismissed Paxton's suit as "a publicity stunt”.
"Mr. Paxton’s actions are beneath the dignity of the office of Attorney General and the people of the great state of Texas," she said.
Earlier this week the Supreme Court rejected a lawsuit that wanted mail-in ballots in Pennsylvania thrown out.
Mr Trump has thrown his support behind the lawsuit and called it “the big one”.
“We will be INTERVENING in the Texas (plus many other states) case. This is the big one. Our Country needs a victory!” Mr Trump wrote on Twitter.
Last month it was reported that the FBI was investigating allegations of abuse of office against of Mr Paxton.