Protests spread across the US after the Supreme Court overturns the constitutional right to abortion

(CNN) - Abortion rights activists across the country are sending a clear message after the overturn of Roe v. Wade: They're not backing down.

From Minnesota to California to Florida, more than a dozen protests are planned Monday to denounce the Supreme Court's decision to eliminate the nearly 50-year-old federal constitutional right to have an abortion.

The fallout was swift: At least 10 states have effectively banned abortion since Friday's ruling.

And 26 states have laws indicating they could outlaw or set extreme limits on abortions, according to the Guttmacher Institute, a research organization that supports abortion rights.

Demonstrations for and against the ruling have been largely peaceful, but a few arrests have been reported.

In Los Angeles, police intervened Saturday when protesters tried to march onto the US 101 freeway.

Officers pushed protesters and struck at least one person with batons, video from the scene shows.

"Full House" actress Jodi Sweetin was pushed to the ground by an officer, video from the incident also shows. Sweetin got up and kept protesting, leading a chant of "No justice, no peace," according to photojournalist and witness Michael Ade. Los Angeles police are aware of the video and the "force used will be evaluated against the LAPD's policy and procedure," the agency said in a statement.

In New York, at least 20 people were taken into custody with charges pending, police said.

In Greenville, South Carolina, at least six people were arrested at a rally Saturday, officials said. The rally included people protesting and supporting the Supreme Court ruling.

In Washington, DC, two people were arrested Saturday after they were accused of "throwing paint over the fence by the US Supreme Court," US Capitol Police tweeted.

In Phoenix, about 1,200 people attended an abortion rights rally Saturday, the Arizona Department of Public Safety said.

Four people were arrested late in the day after a fence around the House and Senate Plaza was torn down, the agency said.

In Lynchburg, Virginia, police are investigating the vandalism of a pregnancy center.

The words, "If abortion ain't safe you ain't safe" were spray-painted near the entrance of the Blue Ridge Pregnancy Center, photos from police show. Security camera footage shows "four masked individuals committing the acts," police said in a news release.

The facility did not immediately respond to CNN's request for comment.

On Friday, the center shared its support of the Supreme Court decision on Facebook, writing: "Rejoicing with an overwhelmed heart of gratitude for the life affirming decisions that were made today."

States ban abortion as others move to protect access

The Supreme Court ruling allowed states to immediately begin setting their own abortion policy, leaving people across the country with varying levels of access.

Nine states now have outright bans on abortions, with varying exceptions or none at all.

They are: Alabama, Arkansas, Kentucky, Louisiana, Missouri, Oklahoma, South Dakota, Utah and Wisconsin.

In Ohio, a six-week ban went into effect went into effect following the Supreme Court decision Friday.

A six-week ban in Texas went into effect last year.

States with abortion bans expected to take effect in the coming days and weeks include Wyoming, Mississippi, Tennessee and Idaho.

In Arizona, abortion providers started canceling appointments immediately after Friday's ruling.

The state Senate Republican Caucus issued a memo demanding the state immediately enforce a pre-Roe law that bans most abortions unless the procedure is necessary to save the life of a mother.

Meantime, some Democratic governors are trying to protect access to abortion.

In Wisconsin, Gov. Tony Evers said he'd fight "with every power we have" after his Republican-controlled state legislature declined to repeal the state's 1849 law banning abortion, which is taking effect again following the Supreme Court ruling.

In California, Gov. Gavin Newsom signed a law Friday protecting non-California residents seeking reproductive health care in the state.

It also protects anyone performing, assisting or receiving an abortion in the state from any potential civil action originating outside the state.

Gov. Tim Walz of Minnesota issued an executive order Saturday providing similar protections. "Our administration is doing everything we can to protect individuals' right to make their own health care decisions," Walz said in a statement.

In Washington, Gov. Jay Inslee promised to create a "sanctuary state" for reproductive choice for people across the country via an upcoming executive order.

The order will direct state police not to comply with extradition efforts from other states seeking to penalize those who travel to Washington to get an abortion.

Inslee did not specify when the executive order will be issued or when it will take effect.

The post-Roe legal battles have started

Shortly after Utah banned most abortions, Planned Parenthood filed a lawsuit claiming the newly enacted law violates civil liberties guaranteed in the state's constitution -- including the right to determine family composition and equal protection.

In the lawsuit, Planned Parenthood said the law will have a disparate impact on women as opposed to men and violates the right to bodily integrity, involuntary servitude, as well as the right to privacy.

The suit names the governor and the attorney general among the defendants.

Performing an abortion in Utah is now a second-degree felony in almost all cases, according to the lawsuit.

Utah's law allows for abortion if there is danger to the mother's health, uniformly diagnosable health conditions detected in the fetus or when the mother's pregnancy is the result of rape or incest.

The lawsuit names Utah's governor and attorney general among the defendants.

"When the Act took effect, PPAU (Plaintiff Planned Parenthood Association of Utah) and its staff were forced to immediately stop performing abortions in Utah beyond those few that are permitted by the Act," the lawsuit reads. "If relief is granted in this case, PPAU's health centers would resume providing abortions that would not qualify for any of the Act's exceptions."

Gov. Spencer Cox's office did not immediately respond to CNN's request Saturday for comment on the lawsuit.

Attorney General Sean Reyes' office told CNN it had no comment on the lawsuit.