"Yet we have resisted the urge to speak out, because this is not the time for us to lecture. It is time for us to listen. It is time for America to examine our tragic failures -- and as we do, we will also see some of our redeeming strengths," the statement said.
Chauvin was charged with third-degree murder. All four officers involved have been fired and investigations are ongoing.
Protests that began in Minnesota have multiplied across the country and around the world. While many have featured peaceful demonstrators marching -- sometimes with police officers -- some have grown violent and destructive, prompting cities to establish curfews and governors to call up the National Guard.
On Monday, as protesters in Lafayette Park next to the White House were being cleared from the area, President Donald Trump came to the Rose Garden to call himself the "law and order" president, saying "domestic terrorism" was to blame for the unrest.
"As we speak, I am dispatching thousands and thousands of heavily armed soldiers, military personnel and law enforcement officers to stop the rioting, looting, vandalism, assaults and the wanton destruction of property," he said. "We will end it now."
Earlier that day, he also called on governors to use their National Guard military police units to "dominate the streets" and threatened to deploy the active duty military if governors failed to use the National Guard more forcefully.
In his five-paragraph statement, Bush went on to talk about the "shocking failure" that many African Americans, especially young men, are harassed and threatened in the U.S.
"It is a strength when protesters, protected by responsible law enforcement, march for a better future. This tragedy -- in a long series of similar tragedies -- raises a long overdue question: How do we end systemic racism in our society? The only way to see ourselves in a true light is to listen to the voices of so many who are hurting and grieving. Those who set out to silence those voices do not understand the meaning of America -- or how it becomes a better place," Bush wrote.
Former President Barack Obama published an essay Monday on Medium addressing the ongoing protests and how he thinks people can move forward. The "bottom line," he wrote, is that "if we want to bring about real change, then the choice isn’t between protest and politics. We have to do both. We have to mobilize to raise awareness, and we have to organize and cast our ballots to make sure that we elect candidates who will act on reform."
The next moment in American history can be "a real turning point," Obama wrote, if "we can channel our justifiable anger into peaceful, sustained, and effective action."
Bush wrote, "America’s greatest challenge has long been to unite people of very different backgrounds into a single nation of justice and opportunity. The doctrine and habits of racial superiority, which once nearly split our country, still threaten our Union."
"Many doubt the justice of our country, and with good reason. Black people see the repeated violation of their rights without an urgent and adequate response from American institutions," he continued. "We know that lasting justice will only come by peaceful means. Looting is not liberation, and destruction is not progress. But we also know that lasting peace in our communities requires truly equal justice. The rule of law ultimately depends on the fairness and legitimacy of the legal system. And achieving justice for all is the duty of all."
"This will require a consistent, courageous, and creative effort. We serve our neighbors best when we try to understand their experience. We love our neighbors as ourselves when we treat them as equals, in both protection and compassion. There is a better way -- the way of empathy, and shared commitment, and bold action, and a peace rooted in justice. I am confident that together, Americans will choose the better way," he concluded.
Read the statement in full on the George W. Bush Presidential Center website.