(CNN) Democrats in the Virginia state House and Senate took steps this week toward rolling back multiple state abortion restrictions, with each chamber passing its own bill looking to strike down obstacles to the procedure.

Both the state Senate bill that passed Wednesday and the state House bill passed Tuesday would remove regulations requiring abortion seekers to undergo an ultrasound at least 24 hours prior to receiving an abortion and to get counseling on alternatives to abortion. They also strike the requirement that facilities providing more than five abortions per year be designated as hospitals.

The measures are two in a flurry of recent progressive moves by both chambers, which garnered Democratic majorities for the first time in more than two decades during the 2019 elections. Critics of the restrictions argued that they are biased and not medically necessary.

Both chambers' measures passed largely along party lines, with the state House passing its bill 52-45. The state Senate bill divided the chamber 20-20, with Democratic Lt. Gov. Justin Fairfax providing the tie-breaking vote to pass.

State Sen. Jennifer McClellan, who sponsored the bill in her chamber, slammed the restrictions as "unnecessary and onerous," vowing that both chambers' bills together "will soon roll back these medically unnecessary burdens on a woman exercising her constitutional right to access abortion care."

House Majority Leader Charniele Herring, who introduced the House bill, asserted in a statement Tuesday that the restrictions were "not designed to protect women, but rather to suppress their ability to make their own choices regarding their bodies."

"This bill concerns an incredibly important decision that should be left up to a woman and her health care provider," she continued, adding that "all women in the Commonwealth deserve accessible reproductive healthcare services, without medically unnecessary obstacles."

On the state House floor Tuesday, Republicans decried the bill as insufficiently strict. House Republican Caucus Chair Kathy Byron argued that the measure "establishes standards so lax, so casual, that anyone, at any time, almost anywhere, can have an abortion performed by just about anybody."

Both measures remove the requirement that only physicians provide abortions during the first trimester of pregnancy -- a move that would expand the provider pool -- though the bills differ in dictating which other health care providers can do so. The House bill would allow physician assistants, nurse practitioners and certified nurse midwives to perform abortions, while the Senate bill would expand the statute only to allow nurse practitioners.

Looking ahead to either bill potentially reaching Democratic Gov. Ralph Northam's desk, each chamber will assess the other one's measure when they exchange bills for consideration next month and work to reconcile the differences, according to a Democratic aide in the state House.

That could occur as early as the week after the chambers exchange bills or as late as the last week of the regular session, in March, the aide added.