* Protests relatively non-violent so far
* March is led by Iraq war veterans
* Black-clad protesters call for insurrection (Adds details, updates progress of march, changes byline)
By Kyle Peterson and Ann Saphir
CHICAGO, May 20 (Reuters) - Thousands of protesters carried their anti-war message to world leaders at a NATO summit on a steamy Sunday, in a mostly peaceful march led by a group of Iraq War veterans who symbolically gave back their military medals.
During the march, a group of black-clad demonstrators darted toward police lines along the route, and some threw water bottles at officers who pushed back and yelled at them to move along, but there were no major incidents.
Police estimated the crowd at 2,500 to 3,000 people, although it appeared to be larger, in what was the biggest rally so far in the week leading up to the NATO summit. Among them was Chicago-based civil rights leader Rev. Jesse Jackson, who walked in summer-like heat with a few women bearing a sign reading "Afghans for Peace."
Riot police made a bigger show of force and watched the march closely than earlier in the week. They were also more open in displaying their equipment including body armor.
Demonstrators ranged from those in festive costumes and a few parents pushing strollers with babies to others in all black with bandannas over their faces and carrying signs including "Anarchists alliance, D.C."
Demonstrators had little chance of being seen by the world leaders and representatives from some 60 countries at the meeting of the military alliance. The summit site, the McCormick Place convention center, is inside a security zone guarded by tall fences. Protesters were kept blocks away from the convention center.
President Barack Obama, who is hosting the summit in his hometown, kicked off the meeting by greeting NATO members one by one. NATO leaders are seeking to chart a path out of the unpopular war in Afghanistan.
The Coalition Against NATO-G8, the group behind Sunday's parade that they hoped would draw 10,000 people, advocated for an immediate end to the U.S. role in the Afghan war.
Other protesters, including participants in Occupy Wall Street demonstrations from around the nation who descended on Chicago for the summit, decried U.S. defense spending and economic inequality.
The protesters hoisted flags and signs, including one pink hand-painted sign shaped like a woman's torso reading "Bust Up NATO." A woman fanned herself in the midday 90-degree (32 C) heat with a "No War, No Peace" sign.
In a brief skirmish, some black-clad, bandanna-wearing protesters pushed and screamed at police.
Some of the black-clad youths yelled at a group of veterans folding a flag, chanting "Burn it!" Some of the youths tussled with other protesters who blocked their path.
Some protesters carried large U.S. flags, some held upside down. Groups of drummers pounded away and Occupy Chicago anti-Wall Street protesters wore clown makeup.
At the outskirts of the protest rally, police clambered out of vans and buses. Dozens of officers on bicycles that have been employed extensively against protests so far this past week were at the ready.
Matt Howard, a former U.S. Marine who served in Iraq, was one of more than three dozen veterans who threw his service medal onto the street near the summit site in a symbol of protest.
Vietnam War veteran Ron McSheffery, 61, said, "I'm in total support of stopping NATO and stopping the slaughter of innocent civilians. If we took the money we spent on bombs and put it into green energy, we wouldn't need to keep the sea lanes open" for oil transport.
Previous protests in the run-up to the summit Sunday and Monday have been lively but peaceful, resulting in fewer than two dozen arrests in the past six days, according to the Chicago Police Department.
"I think we're going to be able to handle it," Police Chief Garry McCarthy told reporters, adding the numbers of demonstrators this week were fewer than many had expected.
"We're going to take care of business. We're well-trained, we're well-equipped. I'll say this again - we're just not going to tolerate illegal behavior."
One officer suffered a concussion Saturday when the police van he was driving was engulfed by a downtown protest. A protester also was hurt when the van sped off.
Five men have been arrested on terrorism-related or bomb-making charges. Three of those charged were plotting to attack Obama's campaign headquarters, police stations and other targets, according to court documents. Defense lawyers said the three were entrapped by police informants.
An affiliate of the computer hacking group Anonymous said it had brought down the website for Chicago's police department and another city website to protest the summit. The websites were back up a few hours later.
Fears that violence would erupt have so far proved unfounded as police have absorbed torrents of verbal abuse screamed at them by protesters. Experts credited the low arrest numbers to restraint by both police and protesters.
McCarthy said at the beginning of the week that his goal was to "extract" those protesters who were provocative and let others demonstrate peacefully. (Additional reporting by Mary Wisniewski and Nick Carey and Eric Johnson; Writing by Andrew Stern; Editing by Greg McCune and Cynthia Osterman)