An anti-gun-violence group is pouring at least $400,000 into a handful of legislative races in hopes of installing a DFL-controlled Legislature that would expand background checks to all gun purchases, including gun shows, internet and other private sales.

Everytown for Gun Safety, a national coalition fighting a political battle against gun rights groups, is spending $100,000 on cable TV ads to try to hold on to an open House seat, take out a GOP suburban incumbent and knock out Senate Minority Leader David Hann, R-Eden Prairie.

In addition to the infusion of advertising cash, Everytown is also supplying field organizers and volunteers through related organizations: Moms Demand Action said it has 1,600 volunteers knocking on doors in three Twin Cities districts, plus one in Rochester and another in Faribault.

Everytown has been active in Minnesota politics since at least 2013, when it hired its first lobbyists in the state. The group was founded by former New York City Mayor Michael Bloomberg, who has contributed tens of millions of dollars of his personal wealth to the cause.

Advocates for gun owner rights won’t be cowed, said Rep. Tony Cornish, R-Vernon Center, who has led the effort to expand gun rights and defeat measures like universal background check legislation at the State Capitol.

“If the Bloomberg types try to influence this election, we’ll kick their butts all the way back to New York City,” Cornish said.

Cornish called Everytown’s efforts “scaremongering” and said background checks would do nothing to stem the tide of gang-related murders in places like the Twin Cities.

“Instead of working on something that would really help, like mental illness, they try to scare people” into giving money, he said.

Everytown cites its own data that in the 18 states with background checks, domestic violence murders and suicides are down 46 percent and 48 percent, respectively.

Along with Hann, the group is targeting Mary Shapiro, a Republican running for an open seat in Minnetonka, and Rep. Sarah Anderson, R-Plymouth.

The National Rifle Association has endorsed Hann and Anderson. The NRA gives Shapiro, a political newcomer, a favorable rating of 86 percent.

This new push in Minnesota came after some DFL lawmakers tried earlier this year to expand background checks on gun purchases, but they were blocked by a long-standing coalition between Republicans and rural DFLers.

Last week, Gabrielle Giffords, the former Arizona congresswoman seriously injured in a shooting in 2011, visited Minneapolis’ battleground suburban areas urging supporters to “never stop fighting.”

The cash from Everytown illustrates a 2016 trend: Without a statewide senate or governor’s race this year, outside groups are pouring money into Minnesota’s legislative campaigns.

Everytown is giving some of the money to WIN Minnesota, a group with a long track record of helping DFLers get elected.

In legislative races that can be decided by just a few dozen votes, the volunteers may be just as important as the money.

Marit Brock, a volunteer director for Moms Demand Action who lives in St. Paul, said she lost her brother to a gun suicide and has two children she wants to shield from gun violence.

She and the other volunteers, who have been out every Saturday for four hours, have focused on independent voters who are neither strongly Republican nor DFL, Brock said.

“We thought if they knew about it, they would be supportive,” she said of the background checks measure. “And, it turns out we were right.”

They ask supportive voters to sign a pledge of support, which they then send back to the person at voting time.

They have nearly 1,000 pledge cards in the five House districts they are working, Brock said.