* Organizers say they want to shut down city next week
* Police chief says department investigating incident
* Crowd cheers call for mayor, police chief resignation (Updates with candlelight vigil, adds quotes)
OAKLAND, Calif, Oct 27 (Reuters) - An Iraq war veteran badly wounded in clashes between protesters and police on the streets of Oakland was awake and lucid, hospital officials and family members said on Thursday.
Scott Olsen, a 24-year-old former U.S. Marine struck in the head during Wall Street protests on Tuesday night, had been upgraded from critical to fair condition overnight.
Olsen's injury has become a rallying cry for the Occupy Wall Street movement nationwide, and Oakland organizers said they would stage a general strike over what a spokeswoman called the "brutal and vicious" treatment of protesters, including the young Iraq war veteran.
At the downtown plaza where he was hurt, several hundred supporters turned out Thursday night for a candlelight vigil in which fellow activists from a group called Iraq War Veterans for Peace addressed the crowd. One drew loud cheers when he said the police chief or mayor should resign.
Olsen "responded with a very large smile" to a visit from his parents, Highland General Hospital spokesman Warren Lyons said at a late-afternoon press conference on Thursday.
"He's able to understand what's going on. He's able to write and hear, but has a little difficulty with his speech," Lyons said.
He said doctors had not operated on Olsen yet and were waiting to see if swelling in his brain eased.
Olsen's aunt, Kathy Pacconi, told Reuters in an email that her nephew was showing signs of improvement.
"I believe he knew his mom and dad were there, and tomorrow he'll be really happy to see his sister, Melissa, because they are really close. Hopefully, he'll start to improve with her visit," Pacconi said.
Occupy Oakland organizers said their strike, scheduled for next Wednesday, was intended to shut down the city.
'SHUT THE CITY DOWN'
"We mean nobody goes to work, nobody goes to school, we shut the city down," organizer Cat Brooks said. "The only thing they seem to care about is money and they don't understand that it's our money they need. We don't need them, they need us."
Spokeswomen for the city of Oakland and Mayor Jean Quan could not be reached for comment.
Brooks said a general strike was a "natural progression" following a crackdown by the city of Oakland early on Tuesday morning in which protesters were evicted from a plaza near city hall and 85 people were arrested.
Protesters sought to retake that plaza on Tuesday night and were repeatedly driven back by police using stun grenades and tear gas. It was during one of those clashes that protesters say Olsen was struck in the head by a tear gas canister fired by police.
The hospital has confirmed Olsen was hurt during the protest, but could not say how he was wounded. Acting Oakland Police Chief Howard Jordan had told a news conference his department was investigating the incident.
He said police had fired tear gas and bean-bag projectiles when protesters defied orders to disperse. He also said that some demonstrators had pelted police with rocks and bottles.
Olsen is believed to be the most seriously wounded person yet in confrontations between police and activists since Occupy Wall Street protests began last month in New York.
News of his injury ignited a furor among supporters of the protests. Activists in Oakland and elsewhere took to Twitter and other social media urging demonstrators back into the streets en masse.
More than 1,000 protesters moved onto the streets of Oakland again on Wednesday night as police largely kept their distance.
At Thursday's vigil, Emily Yates, an Army veteran of two tours in Iraq, urged restraint by police and protesters.
"The police claim they were just doing their job. It's all of our job to think before we throw anything at each other," she said.
Steve Morse, 65, a Vietnam War veteran, drew a hearty cheer when he called for the resignation of either Police Chief Jordan or Mayor Quan, both widely criticized as having bungled the city's response to the Occupy Oakland movement.
Organizers said Quan had been invited in an open letter to address the vigil, but she was not present.
Friends say Olsen had been active in several anti-war veterans groups and had joined Oakland protesters in a gesture of solidarity after learning of the police crackdown there.
Keith Shannon, 24, who said he served with Olsen in Iraq, told Reuters his friend suffered a two-inch skull fracture.
Olsen served two tours in Iraq from 2006 to 2010 with the 3rd battalion, 4th Marine Regiment, Shannon said, adding that he and Olsen deployed together and were assigned to a tactical communications unit. (Additional reporting by Dan Whitcomb, Mary Slosson and Emmett Berg; Writing by Dan Whitcomb; Editing by Jerry Norton and Jackie Frank)