The White House a day earlier announced a new policy that will accept 30,000 migrants per month from four nations but crack down on those who fail to use the plan's legal pathways.
"I think what his proposal is going to do is to entice even more people to come here illegally," Abbott said on Fox News' "America's Newsroom."
"Biden talked about the Republicans having no plan. Republicans do have a plan to secure the border. Biden has no plan to secure the border. Americans are angry and frustrated. It's time for Biden to lay out details about how he will stop illegal immigrants coming across our border."
Biden said his policy will grant humanitarian "parole" to eligible migrants from Haiti, Cuba, Nicaragua, and Venezuela.
"Do not just show up at the border. Stay where you are, and apply legally from there," Biden said in a nationally televised address. "Starting today, if you don't apply through the legal process, you will not be eligible for this new parole program."