"House Bill 2 is an important step that will strengthen protections of innocent, unborn life and improve the safety and health of Texas women," Cruz said of the bill in a statement.

The Texas House approved the abortion bill on Tuesday, and Cruz called on the state Senate to press forward on the measure.

"I hope the Texas Senate will take swift action to pass this legislation for the good of all Texas children and their mothers," he said.

The 20-week abortion ban in the Texas legislature gained national attention after state Sen. Wendy Davis (D) held a 13-hour filibuster to block the bill’s passage at the close of last month’s legislative session.

Gov. Rick Perry (R), a supporter of the measure, called the state legislature back to Austin for a special session to again try to pass the bill.

In an interview on MSNBC Wednesday, Davis said another filibuster of the abortion bill would require "a superhuman feat that none of us are capable of, unfortunately" given the number of days left in the new session. 

The Senate is expected to take up the abortion bill sometime between Friday and Monday and it is likely to pass in the Republican-controlled upper chamber.

Cruz thanked Texas lawmakers in his statement for the bill.

"I am incredibly thankful for and proud of the principled leaders in our Texas Legislature and the many Texas groups who have brought this issue to the forefront, refusing to give up on this important legislation," Cruz said.