President Barack Obama on Tuesday said he understood why Americans felt there was a widening racial gulf in the country, but rejected the suggestion that tensions would only get worse.

Speaking at a memorial service for five police officers who were killed in Dallas by Micah Johnson, Obama said Americans could honor the slain officers by better opening their hearts to one another and taking action to confront and root out institutional racism.

Dallas, Im here to say we must reject such despair, Obama said. Im here to insist that we are not as divided as we seem.

There has been a renewed and tense conversation on the relationship between Americans and the police after two black men, Alton Sterling and Philando Castile , were killed last week by officers in Baton Rouge, Louisiana, and St. Paul, Minnesota, respectively. Demonstrations took place across the country after videos of both incidents went viral, and Obama mentioned both Sterling and Castile by name in his comments.

The five officers were killed when Johnson opened fire during a Black Lives Matter protest in Dallas on Thursday. Dallas Police Chief David Brown said Johnson wanted to kill white people, especially white officers. Authorities have not found evidence linking Johnson to any political groups or the Black Lives Matter movement.

Echoing a balance he has struck in the past, Obama on Tuesday praised the work of police officers but said more needed to be done to reduce bias. Insisting that institutions like police departments root out racism, Obama said, is not an attack on cops but an effort to live up to our highest ideals.

Obama also said he agreed with Brown, who said Americans were asking police to do too much in the United States.

So much of the tensions between police departments and minority communities that they serve is because we ask the police to do too much and we ask too little of ourselves, Obama said. We flood communities with so many guns that it is easier for a teenager to buy a Glock than get his hands on a computer or even a book.

He held up the lives of the five officers killed and called for Americans to have an open heart with one another.

With an open heart, we can learn to stand in each other's shoes and see the world through each others eyes, he said.

Maybe the police officer sees his own son in that teenager with a hoodie whos kinda goofing off, but not dangerous, he continued. And maybe the teenager will see in the police officer the same words and values and authority as his parents.

There were moments when Obama, nearing the end of his presidency, acknowledged how difficult change has been. He noted multiple times he had spoken at too many vigils for the victims of mass shootings and acknowledged that his words had sometimes been inadequate.

Still, the president remained optimistic that Americans would persevere.

I know well make it because of what Ive seen in my own life, he said.

White House press secretary Josh Earnest told reporters on Tuesday that Obama had stayed up late Monday night consulting Scripture to prepare, and the speech reflects his own writing.

In a show of unity on Tuesday, Obama traveled to Texas with Republican Sens. Ted Cruz and John Cornyn. Former President George W. Bush, who served as governor of Texas before becoming commander in chief, also spoke at the ceremony.

Too often we judge others by their worst example, and ourselves by our best intentions," Bush said.

Obama last week called the attack on the police officers despicable, and once again called for more gun control.

Obama has consoled the nation several times after mass shootings during his presidency, including emotional addresses after the shooting at Sandy Hook Elementary School in Connecticut, in which 26 people were killed, and following the shooting at Emanuel AME Church in South Carolina, which left nine dead.