(CNN) Austin, Texas, will set aside city funds for abortion support resources, echoing efforts by other progressive strongholds despite a new state law barring cities from paying for abortions.

An amendment in the city's 2020 budget will set aside $150,000 for "logistical and supportive services for abortion access" such as "transportation, child care, case management, and other services as needed," the amendment reads. The amendment was added to the budget with only one objector before the council -- which includes the mayor as a voting member -- passed the budget overall 10-1 on Tuesday.

The move by Austin, a Democratic hub in a red state that some analysts say could turn bluer in 2020, highlights abortion protection efforts made by local legislatures independent of state policies. In June, New York became what abortion activists called the first city in the country to provide funding for abortions.

Austin Mayor Pro Tem Delia Garza, who introduced the amendment, told CNN on Monday that "because of these continual barriers that our state puts in front of women for a procedure that is legal, for me this is about the access."

"The symbolic part of it is also important: We support women, we support their choices and we're doing what we can, where we can, so that we can access the full spectrum of heath care, including abortion," she added.

Austin City Council member Jimmy Flannigan, the only dissenter to both the amendment and the budget, said following Tuesday's meeting that he supports abortion rights but the amendment's services are the responsibility of the county health care entity, which does not face the same tax caps as the city.

"For me, it really is about how it's the city that the community goes to for everything, and that's just not sustainable," he said.

Austin Mayor Steve Adler praised how the amendment would "help ensure Austinites can make the best choices for themselves and their families," referencing "challenges people are facing as a result of state and federal laws that make it difficult for families seeking an abortion."

Austin is unable to explicitly fund abortions, as Texas law SB22, which bans financial relationships between state entities and abortion providers, went into effect last week.

Garza says she is not concerned with running afoul of SB22, as the law applies only to abortion providers and affiliates, and the amendment explicitly excludes them from accessing the funds.

But abortion-rights opponents slammed the new Austin measure as antithetical to SB22.

"It's appalling that the city of Austin doubled down on its policies to 'save the trees, kill the children,' " Nicole Hudgens, director of policy at the anti-abortion group Texas Values, told CNN after the amendment passed. "This budget amendment is a political stunt attempting to circumvent the law, and if the city really wants to help women, they need to lower their taxes."

Her group testified against the amendment during a city council meeting last month, she said, accusing the council of lacking transparency and of bucking SB22's efforts to "come into alignment with state and federal law." Council members announced the amendment at a press event in mid-August.

John Seago, legislative director at Texas Right To Life, said Monday that while the council was "clear to read the letter of the law and make sure it's compliant, the spirit of the law (SB22) is that we're not going to spend taxpayer dollars to support the abortion industry."

Texas Right To Life supported SB22 and voiced opposition to Austin's abortion support amendment to the council, Seago said. He pointed to the nearly $80 million that the state had set aside over the next two years for its "Alternatives to Abortion" program -- which provide counseling, coordination of prenatal and young child programs, and material resources -- as a better use of funds.

"The Legislature wants to spend money on helping pregnant women and families through things like adoption, maternity homes, pregnancy resources centers and other social services -- in addition to just saying no to pay for the abortion," Seago said.

Austin council member Greg Casar, who helped draft the amendment, sees it as the council's job to fight back against abortion restrictions coming out of the state Legislature.

"Every day, anti-abortion extremists at the Legislature wake up and think about how to restrict access to abortion and health care and to other basic services," he said. "So our job as a progressive city should be to wake up saying, 'How do we expand access to abortion care and health care in the face of a Legislature that is trying to restrict access to those things?' "

He said the amendment would be structured as a competitive grant for nonprofits that provide services like transportation and child care for those seeking abortions.

Citing potential missed workdays from Texas' mandatory 24-hour waiting period before an abortion and out-of-pocket costs from restrictions on health insurance coverage for elective abortions, "these financial barriers make it increasingly difficult for low-income people to access their rights under the law," Casar said.

Advocates say these types of city-level initiatives in New York and Austin could set a new example for how to advance abortion-rights policy as a slew of states advance bills restricting abortion access.

The Texas-based Lilith Fund, which helps Texans pay for abortions, first approached city officials to work on a measure early this summer, after Alabama advanced its near-total abortion ban, said group Executive Director Amanda Williams.

"It was very evident that there was this interest in fighting back and taking a stand against the abortion bans that were sweeping the South, in particular Alabama," she said.

The amendment is "the first in the nation that we know of to offer funding for practical support for abortion access," she added. "It's a way that we can pave the way for other cities to act. ... It's the first, and we're hoping it's not the last."

Andrea Miller -- president of the National Institute for Reproductive Health, which advised advocates on the measures in New York and Austin -- says abortion advocacy on the local level is an "undertapped opportunity."

While the Supreme Court and federal government "may feel difficult to influence right now, people can and should look to their state and local officials and candidates, and there is the possibility for moving forward and mitigating the kind of harm we're seeing by working locally," Miller added.