A day after taking part in the March for Our Lives, Gov. Phil Murphy said Sunday morning that he "walked away with optimism" but warned that "we can't underestimate" the National Rifle Association.

The Democrat also said the fight for more gun control is not just about ending school shootings but the "daily drumbeat of violence" in cities like Newark.

"This ain't over," Murphy said during an appearance on New York City radio station WBLS 107.5-FM. "This is one major step in the right direction. But there are a lot of steps to come. And elections have consequences."

Hundreds of thousands of people took part in marches across the world Saturday to call for more gun-control laws in the wake of the Parkland, Florida school shooting and other recent gun massacres.

Murphy spoke at a march in Newark, the most populous city in New Jersey.

During the radio interview. Murphy repeated his vow to "sign all the gun laws" his Republican predecessor, Gov. Chris Christie, vetoed.

Six bills to tighten New Jersey's gun laws are up for votes in the state Assembly on Monday. Hours after his speech Saturday, Murphy released a statement promising to sign them into law.

But Murphy said Sunday there needs to be new national laws because 80 percent of gun crimes committed in New Jersey come from out of state.

Gov. Phil Murphy speaks Saturday at the Newark March for Life rally.

He suggested that means fighting against the NRA, which he called "the most successful lobbying group in the history of our country."

"We have to hold Congress' feet to the fire," Murphy said. "The NRA is a formidable foe. We cannot underestimate them. I think if the next generation stays with it, we will break their back and beat this lobby."

Meanwhile, a caller told Murphy that gun violence happens more frequently in cities. The governor said the new laws need to address all of it.

"God bless every life lost to gun violence," Murphy said. "Period, full stop."

The NRA opposes new gun laws, saying they would violate the Second Amendment of the U.S. Constitution and make it harder for people to protect themselves.

The group is scheduled to co-host a rally in Trenton on Monday morning to protest the "unconstitutional" bills up for votes Monday -- measures the organizers say are "trying to be forced" through the New Jersey Legislature.

Many Republican lawmakers often oppose more gun-control legislation for similar reasons.

Amid the marches Saturday, the NRA took to social media to denounce the movement.

"Stand and fight for our kids' safety by joining NRA," the group said in a video on Facebook. "Today's protests aren't spontaneous. Gun-hating billionaires and Hollywood elites are manipulating and exploiting children as part of their plan to destroy the Second Amendment and strip us of our right to defend ourselves and our loved ones."

Brent Johnson may be reached at bjohnson@njadvancemedia.com. Follow him on Twitter @johnsb01. Find NJ.com Politics on Facebook.