Trump leads the pack with 32 percent support, according to a Fox News poll.
Trump leads in a nationwide poll with 39 percent support.
He accused Rubio of not standing with him when there was a chance to defund the abortion provider.
The billionaire businessman leads the GOP field with 34.5 percent.
But Cuban said he makes a bigger difference as a private entrepreneur.
The suit was filed in federal court in Alabama on Feb. 3.
Twelve percent want him to be 2016 GOP nominee, tied for first and up 7 percentage points.
The Iowa lawmaker said both parties can improve in offices they already hold.
Trump leads the field with 35 percent support, up 8 points from November.
The fight comes ahead of Saturday night's GOP primary debate.
The ad features Jamiel Shaw, whose 17-year-old son was killed by an illegal immigrant.
Amy Lindsay said she is still considering voting for the Texas senator.
Trump previously promised not to bring a suit against Cruz.
"Free healthcare, free everything," the Republican presidential candidate said.
Former Florida Gov. Jeb Bush and Sen. Rand Paul (Ky.) run a close second.