WASHINGTON — Supreme Court nominee Elena Kagan won praise from skeptical senators in both parties Thursday, building momentum toward what for now appears a smooth road to confirmation this summer.

Kagan, in her second full day of private one-on-one meetings on Capitol Hill, scored points for candor with one-time critic Sen. Arlen Specter, D-Pa., and convinced Republican Sen. Scott Brown of Massachusetts that she’s a strong supporter of the military, despite her move as law school dean to bar its recruiters from Harvard’s campus.

Neither senator committed to voting for Kagan, the solicitor general who President Obama has tapped to succeed retiring Justice John Paul Stevens. But the positive reviews suggested Kagan is making a strong case for herself as she calls on the senators whose votes she’ll need to be confirmed.

“It was a very good meeting, and I think she was very forthcoming,” said Specter, who is days from a tough primary election in which his Democratic opponent has made an issue of his vote last year against confirming Kagan to her current post.

The Pennsylvanian, who was a Republican back then, has said he opposed her because she wouldn’t answer questions about how she’d approach cases. In Thursday’s meeting, however, he said Kagan was far more responsive, even criticizing a January Supreme Court ruling that upheld the First Amendment rights of corporations and labor unions to spend money on campaign ads, thus enhancing their ability to influence federal elections.

“She said she thought the court was not sufficiently deferential to Congress,” Specter said outside his Capitol office after the session. He called her “a good candidate” with excellent credentials.

Kagan also made headway with Brown, who opened their meeting by raising concerns about the military recruitment flap. Kagan barred recruiters because she opposed the military’s “don’t ask, don’t tell” policy for gay members of the armed services.

“It was very clear to me after we spoke about it at length that she is supportive of the men and women who are fighting to protect us, and very supportive of the military as a whole,” said Brown, a military lawyer in his state’s Army National Guard. “I do not feel that her judicial philosophy will be hurting the men and women who are serving.”

The exchanges came on Day 2 of what promises to be a grueling series of face-to-face meetings with senators, where she’s being quizzed on everything from her resume to her writings to her views on hot-button issues like abortion and free speech.