President Trump is focusing on three prospective Supreme Court nominees, sources said Thursday, with conservatives divided on the pro-life records of the candidates who have emerged.

Sources familiar with the selection process say Mr. Trump, after speaking with six judges, is looking in particular at federal appeals court judges Brett Kavanaugh, Amy Coney Barrett and Raymond Kethledge.

“I am thrilled with all those names,” said Carrie Severino, chief counsel of the conservative Judicial Crisis Network. “Trying to figure out which one of those to pick is a great problem to have.”

With Mr. Trump’s announcement coming Monday to fill the seat of retiring Justice Anthony M. Kennedy, some conservatives are taking aim at Judge Kavanaugh, of the Circuit Court of Appeals for the District of Columbia, for rulings on abortion and Obamacare.

“Absolutely, there is cause for concern” about Judge Kavanaugh, a prominent conservative activist said on condition of anonymity.

In a ruling last year, Judge Kavanaugh sided with the administration in the case of a pregnant immigrant teen, who crossed the border illegally, and sought an abortion. He ruled in the minority, which would have prevented her release from federal custody. He criticized the majority’s ruling for creating “a new right for unlawful immigrant minors in U.S. government detention to obtain immediate abortion on demand” and said he would have given the government more time to find a sponsor for the girl.

But some pro-life groups take issue with Judge Kavanaugh for not joining in a separate dissent from Judge Karen LeCraft Henderson, who wrote that the teenager had no right to an abortion because she was not a citizen and had entered the country illegally.

And some conservatives fault Judge Kavanaugh’s 2011 ruling on Obamacare, in which he dissented from the majority decision upholding the law but did so on jurisdictional grounds rather than the merits. As a former member of the George W. Bush administration and a longtime judge on the D.C. appellate court, he is also seen by some detractors as a Washington insider.

Judge Kavanaugh also has his defenders, among them Matt Schlapp, president of the American Conservative Union and CPAC.

“I want to hit the critics head-on,” Mr. Schlapp wrote Thursday in an op-ed for The Hill. “A few conservatives have raised concerns that Judge Kavanaugh will be ‘another John Roberts,’ who sounds great but lets down conservatives in the end … the Kavanaugh-Roberts comparison is completely misplaced.”

He said Judge Kavanaugh has a 12-year record on the appeals court, much longer than Chief Justice John G. Roberts Jr., and his rulings show “dozens of textualist and originalist opinions.”

“Kavanaugh is not another Roberts; he’s another Scalia, Alito, or Gorsuch,” he wrote, referring to conservative justices.

Several pro-life groups are supporting Judge Barrett, including the American Family Association, a nonprofit organization promoting fundamentalist Christian values. The group has written to Mr. Trump with the Judicial Action group urging her appointment and calling her a “known quantity.”

They also said she has a “compelling personal story that pre-empts the liberal playbook,” as shown in her circuit court confirmation hearing last fall.

“Liberals had a miserable time using their tired playbook of attacks against Barrett’s last confirmation because she has a compelling and compassionate life story,” the groups wrote to the president. “She and her husband have seven children, one with special needs. Several were adopted from Haiti. Attempts to label her an ‘uncompassionate bigot’ will fail.”

Catherine Glenn Foster, president and CEO of Americans United for Life, said Judge Barrett could win support for her “Rust Belt” background — a law school professor from Notre Dame.

“You could see there could be a lot of popular support for her,” Ms. Foster said. “She’s not that Washington insider, not an Ivy Leaguer.”

She also said Judge Barrett is “perhaps more open to re-argument of poorly reasoned decisions,” such as Roe v. Wade, the 1973 Supreme Court ruling that legalized abortion.

Judge Kethledge serves on the Sixth Circuit Court of Appeals; he is a Michigan law school graduate who clerked for Justice Kennedy. Conservatives say he would be a jurist in the mold of Justice Neil M. Gorsuch, another Kennedy clerk whom Mr. Trump appointed to the Supreme Court last year.

Others who were interviewed by Mr. Trump this week were Judge Amul Thapar of the Sixth Circuit, Michigan Supreme Court Justice Joan Larsen and Judge Thomas Hardiman of the Third Circuit Court of Appeals in Pennsylvania.

The president also spoke by phone with Sen. Mike Lee, Utah Republican, although that conversation is now being portrayed essentially as seeking the lawmaker’s advice about the nomination, rather than a formal job interview.

Republican Sen. Ted Cruz of Texas said Mr. Lee is “battle-tested, ready, and willing to serve.” In an op-ed for Fox News, Mr. Cruz said his colleague won’t “bend his principles” and is in the mold of Justice Clarence Thomas and the late Justice Antonin Scalia.

“No other candidate has his combination of record, ability, and a sure-fire path to confirmation — and no other candidate would excite conservative voters this November more than someone they know and trust, like Mike Lee,” Mr. Cruz wrote. “Moreover, Senator Lee safeguards President Trump’s Supreme Court legacy for all-time, because there is not a single soul out there who can doubt that a Justice Mike Lee would remain true to the convictions he has fought for his entire life.”

• Seth McLaughlin contributed to this article.

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