"To those families who've been directly affected by tragedy, please know that Michelle and I and the nation grieve with you," he said.
Obama's remarks came shortly after the news that all four police officers involved in Floyd's death had been charged, and that the officer at the centre of the case would face an upgraded charge of second-degree murder.
"We have seen in the last several weeks, the last few months, the kinds of epic changes and events in our country that are as profound as anything that I've seen in my lifetime," Obama said to kick off the event.
"Although all of us have been feeling pain, uncertainty, disruption, some folks have been feeling it more than others."
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The former president said he had been impressed by police officers across the country who had joined protesters instead of standing against them.
"I know you're just as outraged about the tragedies in recent weeks as are many of the protesters. We're grateful for the vast majority of you who protect and serve," he said.
"I've been heartened to see those in law enforcement who've recognised, 'Let me march along with these protesters. Let me stand side-by-side and recognise that I want to be part of the solution.' And who've shown restraint, and volunteered, and listened.
"You're a vital part of the conversation, and change is going to require everybody's participation."
Obama also took a moment to speak about the coronavirus pandemic.
He said the disease had led to "a disproportionate number of infections and loss of life in communities of colour".
"In a lot of ways, what has happened over the last several weeks is – challenges, structural problems here in the United States have been through into high relief," Obama said.
"They are the outcomes not just of the immediate moments in time, but they're the result of a long history of slavery, and Jim Crow, and redlining, and institutionalised racism, that too often have been the plague, the original sin of our society.
"In some ways, as tragic as these past few weeks have been, as difficult and scary and uncertain as they've been, they've also been an incredible opportunity for people to be awakened to some of these underlying trends. They offer an opportunity for all of us to tackle them."
To close out his opening remarks, Obama called on every single mayor in the United States to review their city's use of force policies.
"I've been hearing a little bit of chatter on the internet about voting versus protest. Politics and participation versus civil disobedience and direct action," he said.
"This is not an either-or. This is a both-and. To bring about real change, we both have to highlight a problem and make people in power uncomfortable, but we also have to translate that into practical solutions and laws that can be implemented.
"I am urging every mayor in this country to review your use of force policies with members of your community, and commit to report on planned reforms. What are the specific steps you can take?"
He also took a moment to address comparisons that have been drawn between the current protests across the country and the "chaos" of the protests and riots in the 1960s.
"Although I was very young when you had riots and protests and assassinations and discord, I know enough about that history to say there is something different here," said the former president.
"You look at those protests, and that was a far more representative cross-section of America out on the streets, peacefully protesting. And who felt moved to do something. That didn't exist back in the 1960s, that kind of broad coalition.
"Despite (some violence), a majority of Americans still think those protests were justified. That wouldn't have existed 50 years ago."
Signing off his town hall, Obama said he was still optimistic about the future despite everything going on.
Obama said some people were marching in the protests who would not have considered it even five or 10 years ago, and that was a sign that progress had been made.
"You have unlikely participants, because all of you have worked so hard to raise awareness," he told the other people on the call.
"That is the progress that has been made. It doesn't mean the problem has been solved.
"We don't have the capacity to eliminate 400 years of racism in one fell swoop."