The law, which is set to take effect October 29th, requires doctors to have admitting privileges at nearby hospitals, only allows abortions in surgical centers and bans the procedure after 20 weeks.
Here's Austin attorney Jim George.
"As of today, if this bill went into effect, no one would have the right to perform an abortion living west of I-35 and east of El Paso, Texas."
The suit seeks injunctions blocking rules mandating that physicians have hospital admitting privileges and limiting medical abortions.
Cecile Richards is president of Planned Parenthood.
"This law is unconstitutional and it interferes with women's ability to make her own private medical decision, and it will absolutely jeopardize women's health and safety in Texas."
The measure passed in the second Special Session after a much-watched Democratic filibuster and protests on both sides of the issue at the Capitol.
One of the bill's sponsors was Rep. Steve Toth, R-The Woodlands.
"If they're merely talking about the issue of some of these Planned Parenthood clinics having to close as a result of having to meet ambulatory center regulations, then why is it that Texas Planned Parenthood doesn't care enough about women to make sure these centers meet basic ambulatory center standards?"
The groups filing today plan to file additional paperwork early next week, asking that the effective date of the new law be blocked.