Washington (CNN) Former Vice President Joe Biden , Massachusetts Sen. Elizabeth Warren and Vermont Sen. Bernie Sanders sit atop the field of Democratic presidential contenders among likely primary voters in New Hampshire, according to a new CNN poll conducted by the University of New Hampshire.

Overall, 24% say they back Biden, while 19% each support Sanders and Warren. The five-point margin between Biden and the two senators matches the survey's margin of sampling error.

No other candidate tested earned more than 1% support.

This is the first time this cycle that CNN and UNH have collaborated on a survey of likely voters in the first state slated to host a primary in 2020.

Mixed results for Biden and Sanders

Comparing these results with those from UNH Granite State Polls conducted earlier this year, the poll suggests mixed results for both Biden and Sanders.

In April's UNH poll, Sanders topped Biden 30% to 18%. Biden's increase in support is surely a positive, but the April poll was conducted before he announced his candidacy for president, and his 24% support in the new poll is about the same as the level of support he held in February. Further, polling conducted by other firms in New Hampshire in May and June found Biden with a wide edge over Sanders, which he appears to have lost. But it's not all a loss for Biden: 45% in the new poll say he is the candidate with the best chance of winning in November, consistent with national polling on the topic and up 20 points among New Hampshire likely voters since April.

The news for Sanders is more clearly negative. His support has dipped 10 points since that April survey, and the share saying he has the best chance of winning in November has fallen from 30% in April to 16% now. Yet he remains widely viewed as the most progressive candidate in the field (40% see him that way, about the same as 36% saying so in April), has lost no ground when voters are asked who is most likable among the candidates (20% say so now, 22% did in April), and comes out on top by a double-digit margin as most trusted to handle both health care and the climate crisis -- two issues frequently cited as most important by likely Democratic primary voters.

Warren, on the other hand, sees positive shifts nearly across the board. She has increased her support in New Hampshire by 14 points since April in the new poll, and the share saying they would not vote for her under any circumstances has dipped from 14% (the highest for any candidate) in April to 8% now (behind Biden, who has been ruled out by 14%). Twenty two percent call her their second choice, up from 14% saying so in April. Warren also edges out Sanders among liberal voters, a group that made up about two-thirds of primary voters in 2016, according to the exit poll . Among that group, 26% back Warren, 20% Sanders, 16% Biden, 11% Harris and 10% Buttigieg.

Harris, broadly viewed as having had the best performance in the first set of Democratic debates a few weeks ago in this poll as well as others, does not appear to have made gains in New Hampshire that are as substantial as her improvement nationwide in the wake of that debate. Her support has risen just a few points compared with the April UNH poll (from 4% to 9%), though she has also increased the share who view her as their second choice (15% in this poll vs. 8% in April). Just 2% say they have ruled her out as an option, the lowest share to say so for any of the top four candidates nationally (14% have ruled out Biden, 8% Warren, 6% Sanders).

Overall, only 16% of likely Democratic primary voters say that they have made up their mind about whom to support at this early stage and 20% are leaning toward a candidate, but nearly two-thirds (64%) say they are still trying to decide. But that's a steep decline in indecision compared with previous Granite State Polls conducted by UNH. As of April, 77% said they were still trying to make up their minds.

Health care a top issue

Health care is a top priority for likely Democratic primary voters in New Hampshire, 20% call it the most important issue to their vote in the presidential primary, followed by 14% naming climate change or the environment, 13% immigration, and 9% who say beating Trump or the Republicans is their top issue.

There is a sharp ideological divide over who likely voters in the state trust more to handle health care. Among liberals, 45% say Sanders is their top choice, 20% Warren and 8% name Biden. But among moderates and conservatives, Biden and Sanders are tied at 22% each, with Warren just a touch behind at 18%. Ideological gaps on the other issues tested in the poll -- the economy, the climate crisis and gun policies -- aren't as wide.

Those who say they are likely to vote in the Democratic primary are far more apt than those likely to vote in the Republican primary to say they are deeply interested in the presidential primaries (57% vs. 41% "extremely interested").

Likely Republican primary voters may be less enthusiastic because the choice they will make isn't shaping up to be much of a contest. Overall, 86% say they currently back President Donald Trump over his only announced major opponent, former Massachusetts governor Bill Weld, while just 7% say they back Weld. A majority of likely voters in this GOP primary contest say they've made up their mind (53%).

Still, about four in 10 (39%) say they'd prefer Trump to run unopposed, while 47% say they'd like him to face at least some opposition in the primaries.

Trump is deeply popular with New Hampshire's likely Republican primary voters, 88% say they approve of the way he's handling his job, and 70% say Trump's performance as president thus far is best described as above average or one of the best presidents.

Overall, among all New Hampshire adults surveyed, 45% say they approve of the way Trump is handling his job as president, 51% say they disapprove.