Sen. Bernard Sanders of Vermont starts 2020 with his best standing yet in the tight Democratic primary for president, enjoying a first-place tie with former Vice President Joseph R. Biden and Pete Buttigieg in Iowa and a slight edge on the field in New Hampshire, according to a poll released Sunday.

The CBS News Battleground Tracker/YouGov poll shows Mr. Sanders, Mr. Biden and Mr. Buttigieg tied at 23% apiece ahead of the Iowa caucuses in February. The poll looks at voters’ first choice for the nominee.

Sen. Elizabeth Warren, of Massachusetts, comes in at 16% and Sen. Amy Klobuchar, a Minnesotan hoping to cater to fellow Midwesterners, nabs 7%.

The poll says Mrs. Warren has slipped in New Hampshire while Mr. Sanders, a fellow New Englander, has surged to a two-point edge over Mr. Biden, 27% to 25%, at the top of the pack.

Mrs. Warren comes in at 18% in the Granite State, Mr. Buttigieg grabs 13% and Mrs. Klobuchar gets 7%.

The poll underscores Mr. Sanders‘ bounceback since suffering a heart attack last fall and his staying power in the race, given his supporters’ loyalty.

The poll shows nearly half of his New Hampshire voters (47%) have definitely made up their minds, compared to just 15% of Biden backers.

Mr. Sanders enjoys similar enthusiasm in Iowa and is gaining the greatest share of first-time caucus-goers.

However, the poll says Mr. Biden continues to be seen as the safe choice in the race, which is often characterized as a singular mission to defeat President Trump.

More than half of Iowa Democrats (53%) say Mr. Biden is a “safe choice” compared to percentages in the low 20s for Mr. Buttigieg, Mrs. Warren and Mr. Sanders.

They’re also most likely to cite Mr. Biden as the candidate who can win against Mr. Trump, with 38% saying so versus 29% for Mr. Sanders.

New Hampshire voters reached a similar conclusion, with 36% saying Mr. Biden would probably win, but have more faith in Mr. Sanders, at 33%, than Iowans do.

All told, the poll reveals a race in which Mrs. Warren has suffered from health care-related attacks from other campaigns, providing an opening for Mr. Sanders— who’s never wavered from a single-payer health system — to flip liberal support to his campaign.

“Two months ago, Warren led Sanders among liberal voters, and now she trails him,” the pollsters said. “As he did in November, Biden continues to lead among moderates.”

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