Tony Dokoupil is pushing back.

The “CBS Evening News” anchor, who has been under intense scrutiny since taking the role in early January, led the signature CBS newscast to an audience of a little more than 4 million during the five-day period ended May 22, according to Nielsen — the first time in weeks the show has captured that level of audience.

The program also notched 605,000 viewers in the advertiser-favorite demographic of people between 25 and 54. The previous week’s “CBS Evening News” captured around 3.8 million viewers and 482,000 in the demographic.

Make no mistake: “CBS Evening News” remains well behind its two main rivals, ABC’s “World News Tonight” and NBC’s “NBC Nightly News.” But at least it’s showing signs of regaining some ground.

ABC’s “World News Tonight” continues to lead the sector handily, with nearly 8.2 million overall viewers and 966,000 in the demo. “NBC Nightly News” won nearly 6.1 million viewers, and 867,000 in the demo.

The ratings for last week appear to be based on four days of broadcasts. ABC and NBC each “retitled” one of the five days’ of broadcasts last week, and it was not immediately clear whether CBS had as well, though it usually drops Fridays from its tabulations. Networks “retitle” specific episodes of their nightly-news programs when they believe some outside factors, like a sports telecast or lower-than-usual viewership will affect the Nielsen measurement of viewership.

The four-million-viewer level has been seen as something of a demarcation point in recent months. Before Dokoupil took the reins of the show, CBS News ran a version of “CBS Evening News” anchored by Maurice DuBois and John Dickerson, hoping that a two-anchor format might generate new interest as Lester Holt ceded the reins of NBC’s “Nightly” to Tom Llamas, It didn’t, and the CBS show shed audience and fell below 4 million viewers on many weeknights.

Dokoupil had gained traction over the years during his time as a co-anchor on “CBS Mornings,” and he won the notice of both former CBS News president Susan Zirinsky and current CBS News editor in chief Bari Weiss. He has demonstrated a proclivity for developing interesting features, and, more recently, for taking on author Ta-Nehisi Coates on whether his writing expressed antipathy for Israel. He has also tried to imbue the evening newscast with a more writerly voice, and has hustled across the nation and to global hot spots in the earliest part of his tenure on the program.

Last week’s “CBS Evening News” telecast included the start of “Affordability in America,” a new series that examines how Americans are coping with rising prices and economic uncertainty. Senior executives attribute the viewer upswing in part, according to a person familiar with the matter, to viewers noticing more of the work of Dokoupil, executive producer Kim Harvey and the rest of the evening newscast production team.