Newport News: Condition of teacher shot by child improving
Abby Zwerner suffered life-threatening injuries after she was shot with a handgun at Richneck Elementary School in the city of Newport News on Friday, Qazet.az reports.
Mayor Phillip Jones told the BBC that Ms Zwerner's recovery was "trending in a positive direction".
But he added that she remained in a critical condition after the incident.
Online, social media users wished Ms Zwerner - who is believed to be in her 30s - a speedy recovery.
Her alma mater, James Madison University in Virginia, offered "prayers and best wishes for Abby's health and recovery".
It is unclear how the child - who remains in police custody - obtained the gun. Officials said that while the school - which has around 550 students - had metal detection facilities, students were checked at random and not every child was inspected.
Police have declined to say what might have motivated the incident, but Chief Steve Drew told reporters the shooting had come after an "altercation" in a first grade (ages six to seven) classroom and did not appear to be "accidental".
One parent, Steve Gonzalez, whose child was present in the classroom at the time of the shooting, told Fox News that Ms Zwerner had reacted selflessly after the shooting.
He said that after being struck by the bullet "she screamed at her kids to run away".
Mayor Jones - who took office just five days ago - said police were continuing to investigate the circumstances around the shooting, but said he thought the "word altercation was a valid one, and one that I would use".
"We don't have all the answers about how a six-year-old was able to handle a firearm or how a six-year-old was able to access a firearm," he said.
"This is a dark day in our history and I think this is a red flag for the country."
Officers have also declined to discuss what contact they have had with the student's parents.
Virginia law prevents six-year-olds being tried as adults. And the child would also be too young to be committed to the custody of the Department of Juvenile Justice if found guilty.
But a judge could revoke the parents' custody of the boy and take him into the supervision of the state.
On Saturday, Chief Drew said police had "been in contact with our commonwealth's attorney [local prosecutor] and some other entities to help us best get services to this young man".
School District Superintendent George Parker said on Saturday that the shooting showed "we need to educate our children and we need to keep them safe".
"We need the community's support, continued support, to make sure that guns are not available to youth and I'm sounding like a broken record today, because I continue to reiterate that: that we need to keep the guns out of the hands of our young people," he added.
Newport News is a city of around 180,000 people and sits about 70 miles (112km) to the south of the state capital Richmond.