WASHINGTON (CNN) -- Thousands of demonstrators rallied Saturday in Washington to demand tougher gun control laws, many describing themselves as first-time capital marchers who've had enough of gun violence.

On a cold day, a vanguard led a blocks-long procession with a big blue banner, declaring "March on Washington for Gun Control: When we stand together, we stand a chance."

The demonstrators want reinstatement of the federal ban on the sale of military-style semi-automatic rifles such as the one used in the recent Newtown, Connecticut, school shooting that left 20 children and six adults dead, plus the gunman and his mother. The protestors also want a ban on the sale of high-capacity ammunition magazines and universal background checks.

Many marchers just carried black-and-white placards bearing the names of victims of gun violence, such as Veronica Soto, a Newtown teacher who was killed in the Sandy Hook Elementary massacre.

Co-organizer Molly Smith highlighted how many demonstrators were ordinary citizens, the organization of whom was assisted by a webpage and Facebook page.

"It's been a remarkable learning experience," Smith told CNN, "the realization that we're citizens and this is an active citizenship, and being a citizen isn't just sitting around and gassing about it."

The march was the first major demonstration since the Newtown mass shooting last month, and it comes two days after Sen. Dianne Feinstein, D-California, introduced a bill that would ban some assault rifles, semi-automatic weapons and high-capacity magazines.

U.S. Education Secretary Arne Duncan told an assembly of marchers, after they reached their rallying area midway between the White House and the Capitol, that Saturday's demonstration wasn't about the Second Amendment.

"This is about gun responsibility; this is about gun safety; this is about fewer dead Americans, fewer dead children," Duncan told the crowd.

He recalled that as the former chief of Chicago Public Schools, he oversaw a system in a city where a student was killed by gun violence every two weeks.

"Far too many of our children are growing up in climates where they are scared," Duncan said. "That has to change."

He added, "This march is a starting point. It's not an ending point. We must act, we must act, we must act."

U.S. Rep. Eleanor Holmes Norton, D-District of Columbia, asked residents of Newtown, Connecticut, to make themselves known in the crowd.

'We came to stand with you and bear witness with you until we vindicate your children and those who died with them," Norton said.

She urged the assembly to press for gun reform.

The demonstrators started chanting: "Yes, we can! Yes, we can! Yes, we can!"

Without mentioning the National Rifle Association, Norton made a reference to the powerful gun lobby, saying, "It comes down to us because we are immune to their lobbying.

"Only an outraged public can end the gun violence that has enveloped our country," she added. "We the people who did not act before, we the people this time will step forward.

"And this time we will not step back."

Colin Goddard survived being shot four times during the Virginia Tech massacre in 2007, the deadliest shooting in U.S. history, one that left 33 people dead, including the gunman, who took his own life.

Goddard, one of the rally speakers, said he was shot above the knee, twice in the hip and once in the shoulder.

"I consider myself one of the lucky ones," he told the gathering.

Then, speaking of subsequent school shootings across the nation, he added: "I kept seeing what happened to me happen to other people."

Goddard now works for the Brady Campaign to Prevent Gun Violence as assistant director for victims advocacy and federal litigation.

One marcher, Lori Bennett, said she wants to make a difference.

"My two older children, of course, are very aware of what's going on and I said, 'I'm going down there, you know, for you, for us, and to make a difference," she said. "Without sounding corny, but I mean, it's just piggybacking on the sentiment of the politicians that are in favor of all this change.

"People as a country, like, we can't keep waiting for all the politicians to make a move," she added.

A small opposing demonstration was held across the street from the gun control advocates' staging area near the Capitol. One gun rights advocate said he thinks people in schools should be armed -- a viewpoint he developed after the Newtown shooting.

"I could not figure out why government employees have armed guards, banks have armed guards to protect the money, but the government, for some reason, thought we don't need armed guards to protect our children," said Dick Heller, who was the lead plaintiff in a 2008 Supreme Court case that overturned a sweeping handgun ban in the nation's capital.

"Maybe they're less worthy. I don't know. I don't know what their thinking was. All I can't understand is why didn't they protect their children like the government protects itself?" Heller added.

The gun control march organizers are also calling on Congress and state legislatures to prohibit the sale of bullets that shatter inside the body and to require gun-safety training for all firearms purchasers.

Among the other placards that demonstrators raised above their heads were: "More guns? More violence" and, in a reference to NRA CEO Wayne LaPierre (who has said "the only thing that stops a bad guy with a gun is a good guy with a gun"): "Hey LaPierre. How about this? Keep the Bad guy from even getting a gun!"

CNN's Emily Schmidt contributed from Washington. Michael Martinez wrote and reported this account from Los Angeles. CNN's Laura Koran also contributed.

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