The federal government — facing multiple lawsuits and a looming court order — has begun releasing a few children to their mothers and fathers, and said Thursday that it plans to reunite nearly 3,000 children by the end of the month.

At least four women in Massachusetts had filed lawsuits against the federal government in recent days, alleging the government had placed unreasonable roadblocks in their paths to reunite with their children, who were taken by the government at the border under President Trump’s “zero tolerance’’ policy.

On Thursday, the government released some of the children named in the lawsuits, and administration officials promised that by the end of the month they would reunite the nearly 3,000 children separated from their parents. That timeline would comply with a federal court order.

The announcement followed weeks of enormous public pressure and heart-wrenching images in the news media over Trump’s family separation policy.

Angelica Rebeca Gonzalez-Garcia, who was separated from her 8-year-old daughter on May 11, was reunited with the girl at Boston’s Logan Airport Thursday afternoon, the day before a judge was scheduled to hear her case. Sirley Silveira Paixao, whose 10-year-old son was sent to a Chicago shelter after being taken from her on May 24, was also reunited with her child Thursday after a judge’s order.

Lidia Souza, who fled Brazil and now lives in Hyannis awaiting an asylum hearing, was reunited with her son in Chicago last week. The fourth plaintiff, who is identified only by the initials W.R. in her lawsuit, is still fighting for custody of her child.

Health and Human Services Secretary Alex Azar said Thursday that his agency would begin using DNA tests on children in the government’s custody to match them with their parents. He vowed to reunite children under 5 with their parents by July 10, a court-imposed deadline, and the older minors by July 26, even if it means bypassing some of the agency’s vetting standards.

“We will comply even if those deadlines prevent us from conducting a standard or even a truncated vetting process,’’ Azar said.

Advocates expressed skepticism that the government would be able to follow through on that promise, given the slow pace of reunification so far.

The four Massachusetts women who filed lawsuits alleged that the government treated them as strangers who needed to apply to “sponsor’’ their children, rather than as parents who simply needed to prove their relationship in order to be reunited with their own children.

In particular, they complained about weeks-long waits to get fingerprinted. HHS recently adopted a requirement that all sponsors of children and members of their households be fingerprinted. The fingerprints are then shared with local, state, and federal authorities, including the Department of Homeland Security, to determine the immigration status and criminal history of the adults, the policy says.

The 35-year-old Brazilian woman who asked to be identified by her initials W.R. due to fear of retaliation for telling her story is suing to get her 9-year-old son released from a Texas shelter.

W.R. has not seen her son since May 30, when she watched Border Patrol agents take him away from the separate, caged-off area for children where he slept in a frigid facility in Arizona. They had crossed the Mexico border after migrating from Brazil.

About three weeks later, she was released on bond, paid by her brother, a resident of Malden, and began the process of trying to get her son released.

W.R. said she filled out a “family reunification packet’’ and submitted more than 40 pages of materials to the Baytown, Texas, shelter run by the Christian nonprofit BCFS where her son was taken. Then, according to the lawsuit, a BCFS case worker interviewed her in late June as a potential sponsor for her son, asking her if she attended a Christian church regularly, how she disciplined her son, and whether she knew the location of local clinics if her son were to fall ill.

“She was much more concerned with my religious practices than my rights as being his mother and my son’s right to be reunited with his mother,’’ W.R. said in an interview.

W.R. and the three other women who sued the federal government were told a recent rule change now requires everyone in the house where they live to be fingerprinted, a process that could prolong families’ separation for weeks. Some were asked to prove they could financially support the child.

“The mother isn’t considered as parent. The mother is being treated as sponsor, as a legal stranger who has to submit an application to receive an unaccompanied minor,’’ said Iván Espinoza-Madrigal, executive director of the Lawyers’ Committee for Civil Rights and Economic Justice, which is representing W.R. with the law offices of Wilmer Hale.

The fact that biological parents were being vetted the same way as potential sponsors seems to bolster the allegation that the government had no plan in place to reunite the families it separated at the border.

“The frustration here is these moms were all fingerprinted coming into the country, and the families we’re working with have birth certificates,’’ said Representative Katherine Clark, whose office assisted Gonzalez-Garcia and W.R. “This should be as easy as getting these children on a plane and returned to these moms.’’

But others said the extra vetting and fingerprinting are meant to ensure that the adults who are given responsibility for the children have clean records — a necessary improvement in vetting those caring for the children. And, they say, it was needed after some children were smuggled into the country to work on a Ohio egg farm, and after recent reports that calls to check on the welfare of some 1,475 immigrant children went unanswered.

“If you don’t like Donald Trump, you don’t like anything he does and you’re going to read some sort of malign motive into whatever he does,’’ said Andrew Arthur, a former immigration judge and resident fellow in law and policy at the Center for Immigration Studies, a nonprofit that advocates for stricter immigration laws. “But this is one of those things where I think HHS is just trying to do a better job.’’

Gonzalez-Garcia, the Guatemalan woman who was reunited with her daughter at Logan, has withdrawn the federal lawsuit, her lawyers said.

She dropped to her knees at the sight of her daughter, opened her arms, and hugged the 8-year-old girl she last saw at an immigration detention center in Arizona. The moment was captured on video tweeted by immigrant advocates.

“Today, I am reborn,’’ she said later during a news conference, one arm tightly around the little girl’s shoulders while the other held her hand. “I thought my life had ended, and I was never going to see my daughter again. I don’t have words to express the happiness that my heart feels.’’

Ronaldo Rauseo-Ricupero, one of Gonzalez-Garcia’s attorneys, said it shouldn’t be so difficult for all parents.

“It shouldn’t take a federal lawsuit for everyone who is similarly situated’’ to be reunited with their children, Rauseo-Ricupero said.

Akilah Johnson can be reached at akilah.johnson@globe.com. Follow her on Twitter @akjohnson1922. Liz Goodwin can be reached at elizabeth.goodwin@globe.com.