Northamptonshire Police was contacted for comment.
Tata said the site would be closed for 24 hours and the position would be reviewed on Wednesday.
“This is a devastating loss, and our thoughts are with all who are grieving,” added Rielly, who is a Labour councillor.
“Corby’s identity has long been shaped by its steelworkers and their families.
“The workforce, and the unions that represent them, are part of the fabric of this town.
“When tragedy strikes at the workplace, it is felt not only across the site but across our whole community.”
“Our community stands together with the family, with the workforce, and with all those affected by this tragic event.”
The steel sector in Corby once employed thousands of workers in the town, but the figure now is about 500.
Employees and campaigners were devastated by the closure of most of its steelworks in the 1970s and 1980s, leading to an unemployment rate of 30% in Corby.
Tubes from the Tata Steel factory have previously been used in structures such the London Eye.