Mayor Michelle Wu is expected to win a majority of votes in Boston’s preliminary mayoral election on Tuesday, easily surpassing her closest competitor, Josh Kraft, a political newcomer who has struggled to gain traction in the race.

Boston holds a nonpartisan preliminary election instead of party primaries, with the goal of winnowing the field of candidates to two; a total of four names are on Tuesday’s mayoral ballot. Both Ms. Wu, a progressive Democrat who is the first woman and person of color to lead the city of 650,000, and Mr. Kraft, a fellow Democrat and philanthropist, will very likely advance to the general election in November.

The race between Ms. Wu, 40, and Mr. Kraft, 58, took a combative tone from the start. Mr. Kraft, a son of the New England Patriots owner Robert Kraft, has assailed the mayor for months with claims that she has snarled city traffic by expanding bike lanes, allowed the opioid crisis to fester unchecked and obscured ballooning costs of a contentious stadium redevelopment project.

Ms. Wu has called attention to her rival’s privileged background and his recent move to the city from its upscale suburbs, criticizing him in a recent statement for his “relentlessly negative campaign and his attempt to buy this election.” Mr. Kraft previously ran the Patriots’ philanthropic foundation and worked for the Boys and Girls Clubs of Boston for 30 years.

For all his forceful criticism of Ms. Wu’s policies, Mr. Kraft has struggled to make headway with voters. A poll released last week by Emerson College showed Ms. Wu ahead of him by an eye-popping 50 points. An Emerson poll in February had her leading Mr. Kraft by 14 points.

One likely factor helping Ms. Wu is President Trump’s repeated threats and actions against Boston, and her refusal to back down. The recent Emerson poll found that two-thirds of city voters supported the mayor’s continuing commitment to Boston’s immigration policies. In particular, Ms. Wu has vocally defended a local ordinance, known as the Trust Act, that limits the role of city officials in helping federal agents detain or deport undocumented immigrants on civil warrants.