Democratic Lt. Gov. Gavin Newsom is maintaining a solid lead in the June 5 primary for governor, with Republican John Cox and Democrat Antonio Villaraigosa in a close fight for the runner-up slot in the top-two primary, according to a new poll by the Public Policy Institute of California.

In the five pre-election polls the nonpartisan institute has taken since December, “the one constant has been Newsom,” said Mark Baldassare, the organization’s CEO and the poll’s director. “His numbers have been very consistent,” ranging from 23 percent in December to a high of 28 percent in March. He’s at 25 percent among likely voters in the new survey.

But the second place spot is just as important, since that finisher will join the leading vote-getter on the November ballot. Cox, a San Diego-area businessman, now leads Villaraigosa, former mayor of Los Angeles, 19 percent to 15 percent. That’s up a bit from Cox’s 15 percent to 13 percent lead in April.

The top three choices are followed by GOP Assemblyman Travis Allen at 11 percent, state Treasurer John Chiang at 9 percent and Delaine Eastin, the former state schools chief, with 6 percent.

Over the past five polls, “the biggest change has been for Cox, who has gone from 9 percent to 19 percent,” said Baldassare. The improving numbers for Cox and, to a lesser extent, Allen can be attributed to Republicans getting more comfortable with the two lesser-known GOP candidates.

That number may be understating Cox’s current support, since much of the poll was taken before President Trump endorsed Cox on Friday.

About two-thirds of Republicans are backing either Cox or Allen, with 14 percent undecided. Among Democrats, Newsom has support from 42 percent, with Villaraigosa at 19 percent, Chiang at 11 percent and Eastin with 9 percent.

Independent voters are split almost equally among the four leading candidates.

While independents in California are more likely to lean Democratic, they’re more moderate than rank-and-file Democrats, Baldassare said.

“They’re likely to be the wild card in the primary election,” he said.

Overall, about 15 percent of likely voters are undecided, which isn’t unusual for a statewide primary at this stage of the race, Baldassare said.

The PPIC poll was one of two major surveys released this week. A USC Dornsife/Los Angeles Times poll released Wednesday found Newsom on top among likely voters with 21 percent, followed by Villaraigosa at 11 percent and Cox at 10 percent. A whopping 39 percent of voters were undecided.

In the race for the Senate, Democratic Sen. Dianne Feinstein holds an overwhelming lead in the PPIC survey in her bid for a fifth full term. The former San Francisco mayor leads Los Angeles state Sen. Kevin de León, a fellow Democrat, 41 percent to 17 percent, with 36 percent undecided.

No Republican candidate for Senate was listed by name in the poll, since none of the 11 on the primary ballot met the survey’s qualification of raising at least $100,000 and having a visible campaign organization, Baldassare said.

“Republicans are baffled about what to do,” he said. “They’re unhappy without a high-profile candidate.”

Among Republicans, 59 percent are still undecided about whom to back in the Senate race, with 59 percent also unhappy with their choice of candidates. The numbers weren’t much different for independents, with 47 percent undecided and 53 percent dissatisfied with the ballot lineup.

The poll’s look at California congressional elections, however, provided some worrisome numbers for Democrats looking to flip seven or more GOP-held seats to help the party take back control of the House.

While not looking at individual contests, the survey found Republicans are favored by a 60 percent to 32 percent margin in GOP-held districts. More ominously for Democrats, those numbers didn’t change much in 10 competitive districts.

In those competitive House districts, 62 percent of likely voters would rather see a candidate who would work with the Trump administration than push back against the president.

Voters in many of those competitive districts “may have supported a Democrat for president two years ago, but this is a different election,” Baldassare said. “There’s a lot of work ahead for Democrats.”

The poll is based on telephone surveys of 1,702 California adults, including 901 likely voters. It was taken May 11-20 and has a margin of error of plus or minus 4.1 percentage points for likely voters.

John Wildermuth is a San Francisco Chronicle staff writer. Email: jwildermuth@sfchronicle.com Twitter: @jfwildermuth