Brown, a black teenager, died after being shot at least six times by Darren Wilson, a white police officer, on August 9. The 18-year-old's body was left in the street for several hours before being taken away.
Police Chief Thomas Jackson said he took responsibility for "any mistakes I have made."
Addressing Michael Brown's family, Jackon said: "No one who has not experienced the loss of a child can understand what you're feeling. I'm truly sorry for the loss of your son. I'm also sorry that it took so long to remove Michael from the street."
"It was just too long and I'm truly sorry for that. Please know that the investigating officers meant no disrespect, they were simply trying to do their jobs," Jackson said.
Brown's death triggered days of sometimes violent protests and a renewed national debate on racial discrimination within the American justice system. It came two years after the 2012 killing of Trayvon Martin, a Florida teenager who was shot dead by neighborhood watch volunteer George Zimmerman.
There are conflicting accounts of the circumstances of Brown's death. Police claimed that Brown, accused of stealing a box of cigars, was shot after a struggle with police officer Wilson.
But witnesses say Brown put up his hands to surrender before Wilson opened fire. Wilson has been placed on administrative leave pending an investigation.
Ferguson is a suburb of St. Louis with a population of 21,000 - the majority of whom are African American. The police force and town council are overwhelmingly white.
Apology to protesters
Police Chief Jackson also apologized to those who felt their constitutional right to protest had not been protected. Demonstrations against Brown's death led to hundreds of arrests, with some protesters complaining that police used undue force against them.
The violence prompted Missouri Governor Jay Nixon to briefly call in the National Guard to bring the protests under control.
"The right of the people to peacefully assembly is what the police are here to protect," Jackson said.
"If anyone who was peacefully exercising that right is upset and angry, I feel responsible and I am sorry. I'm also aware of the pain and the feeling of mistrust felt in some of the African-American community towards the police department," he added.
"It is clear we have much work to do."
Obama acknowledges racial problems
US President Barack Obama spoke about Ferguson during his Wednesday address to the UN General Assembly in New York, admitting to racial problems and tensions.
"I know the world also took notice of the small American city of Ferguson, Missouri, where a young man was killed, and a community was divided," Obama said.
"We have our own racial and ethnic tensions. And like every country, we continually wrestle with how to reconcile the vast changes wrought by globalization and greater diversity with the traditions that we hold dear."
jr/kms (dpa, AFP)