Washington (CNN) Supreme Court nominee Brett Kavanaugh on Wednesday described Roe v. Wade's right to abortion as settled -- "important precedent" -- yet he has also narrowly interpreted when a woman can exercise that right.

His past views, reinforced by testimony before the Senate Judiciary Committee, suggest Kavanaugh would permit government to impose stricter regulation of abortion, for example, with additional requirements that could delay the procedure or in stiffer rules for physicians who would perform it.

With the departure of retired Justice Anthony Kennedy, abortion rights could hang on Kavanaugh's vote. His critics have warned that with a new ninth justice Kavanaugh, the court would outright reverse the 1973 milestone that made abortion legal nationwide.

If Roe is overturned, abortion law would be set on a state-by-state basis, as President Donald Trump, who nominated Kavanaugh, declares he wants.

In a memo Kavanaugh wrote in 2003 which was made public Thursday, he acknowledged that the Supreme Court "can always overrule" Roe v. Wade.

"I am not sure that all legal scholars refer to Roe as the settled law of the land at the Supreme Court level since Court can always overrule its precedent," he wrote, adding that some conservative justices then on the court "would do so."

Roe and abortion rights are not an all-or-nothing proposition.

Even as Chief Justice John Roberts and Justice Samuel Alito, for example, have not voted to overturn Roe, they have narrowly interpreted its breadth and declined to strike down tough state restrictions on abortion.

Roberts and Alito were among dissenting justices as the Supreme Court in 2016 -- with Kennedy's crucial vote in the majority -- invalidated Texas regulations on clinics and physicians that performed abortions.

On Wednesday, under questioning from Democrats, Kavanaugh declined invitations to promise he would not vote to reverse Roe, saying it would violate judicial norms to promise a vote on any particular case.

"As a general proposition I understand the importance of the precedent set forth in Roe v. Wade," Kavanaugh said.

But perhaps more revealing, as he expressed regard for Roe and a 1992 decision (Casey v. Planned Parenthood of Southeastern Pennsylvania) that reaffirmed Roe, Kavanaugh elaborated on why he dissented when his US appeals court allowed a 17-year-old woman to end her pregnancy, over objections from the Trump administration.

Kavanaugh had declared that the DC Circuit majority's opinion would lead to a new right for "immediate abortion on demand."

His testimony Wednesday on the case, first in an exchange with Sen. Dick Durbin, offered a window into his thinking. As the Illinois Democrat asserted Kavanaugh would impose a new requirement to a woman's exercise of the abortion right, Kavanaugh emphasized his concern for the young woman who was being held in a US detention center in Texas.

"She's in an immigration facility in the United States. She's from another country. She does not speak English. She's by herself," Kavanaugh said, defending his view in Garza v. Hargan that the Trump administration could require her to find a sponsor before obtaining an abortion. Kavanaugh said the teen could have been able to "consult with" the sponsor as she faced her decision.

The DC Circuit majority found that the Trump administration was imposing an "undue burden" on the woman, violating her constitutional right.

"The government's conduct in the case had already forced her to delay her decision on an abortion by several weeks," Durbin told Kavanaugh.

Kavanaugh responded that he had turned to Supreme Court precedent testing laws that require a teenager to notify or get permission from a parent before obtaining an abortion. In his dissent, Kavanaugh acknowledged that, "Those laws, of course, may have the effect of delaying an abortion."

The DC Circuit majority read Supreme Court precedent differently because the 17-year-old who had crossed the southern border had already fulfilled the requirements of state law for a minor trying to obtain an abortion. A Texas court had determined that she could decide what was in her best interests.

Kavanaugh had written that the administration was not forcing the young woman to obtain consent from a sponsor. "It is merely seeking to place the minor in a better place when deciding whether to have an abortion," he said.

As Durbin noted that other judges read abortion-rights differently, Kavanaugh added, "I did the best to follow precedent ... I did my level best in an emergency posture, I had basically two days to do this case."

In separate questioning on Wednesday, Democratic Sen. Richard Blumenthal noted that Kavanaugh, a 12-year veteran of the DC Circuit, was not on Trump's list of Supreme Court candidates until November 2017, one month after his dissenting opinion in Garza v. Hargan. The Connecticut Democrat said it looked as if Kavanaugh landed on the list because of his view blasting what Kavanaugh described as "abortion on demand."

Kavanaugh rejected that idea. He said he believed Trump added him to the list because "a lot of judges and lawyers I know" urged the consideration "based on my record from the past 12 years."