Under the rules of the Iowa caucuses, many voters who support less popular candidates will have to back someone other than their top choice in the final balloting. Ms. Warren has strength in this regard: She is by far the most popular second-choice pick among voters, with 23 percent naming her as their personal runner-up, according to the poll. No candidate enjoys a higher favorability rating than Ms. Warren, who is seen positively by 73 percent of likely caucusgoers.

Still, when voters were asked to choose from among only the top four candidates, it was Mr. Sanders and Mr. Buttigieg who benefited the most. In this scenario, Mr. Biden, Mr. Buttigieg and Mr. Sanders were all bunched up in the mid-to-high 20-percent range, while Ms. Warren’s support was at 16 percent.

The Iowa Democratic electorate remains focused mostly on domestic issues, with 45 percent calling health care their top concern and another 18 percent naming either jobs or income inequality, according to the Monmouth poll.

But with President Trump embroiled in a tense standoff with Iran this month, some voters have also turned more attention to foreign policy. The share of likely caucusgoers who named international affairs as their main focus jumped by 10 points since November, to 16 percent.

Also on Monday, Quinnipiac University released a national poll that showed Mr. Biden at the top of the heap, with 25 percent support among Democratic voters nationwide, followed by Mr. Sanders at 19 percent and Ms. Warren at 16 percent. Mr. Buttigieg commanded just 8 percent nationwide. Since the primaries and caucuses take place over a series of months, the national picture is almost certain to shift as the season continues.