New Orleans (CNN) President Barack Obama returned Thursday to an outwardly thriving New Orleans to mark strides 10 years after Hurricane Katrina slammed into the city.

But underneath the visible recovery lie persistent racial and economic inequities that haven't receded since the storm -- figures Obama said prevent New Orleans from declaring itself fully recovered a decade after Katrina.

"Our work here won't be done when almost 40% of children still live in poverty in this city. That's not a finished job. That's not a full recovery," he said, going on to cite statistics showing African-American households in the city earn more than 50% less than their white counterparts -- a figure well above the national average.

Obama: There is still grief in our hearts after Katrina

Obama: There is still grief in our hearts after Katrina 03:08

Obama: There is still grief in our hearts after Katrina

"There's still too many people who haven't been able to come back home," Obama said. By some estimates, more than 100,000 African-Americans fled New Orleans following Katrina, never to return.

Obama said Thursday there are "folks around the country every day (who) live the words sung by Louis Armstrong: 'Do you know what it means to miss New Orleans?'"

The barometers of racial inequality Obama cited aren't unique to New Orleans, and haven't dampened the city's enthusiasm for what has otherwise been a steady recovery that includes new construction, jobs and visitors.

But the now-chronic gaps between rich and poor, and whites and blacks, provided a sober backdrop for Obama's tour of the hard-hit Treme and Lower Ninth Ward neighborhoods on Thursday, where he spoke with residents and assessed the district's recovery.

On Thursday, he argued Hurricane Katrina "started out as a natural disaster" but "became a man-made one -- a failure of government to look out for its own citizens."

"What that storm laid bare was another tragedy -- one that had been brewing for decades," Obama said. "New Orleans had long been plagued by structural inequality that left too many people, especially poor people, especially people of color, without good jobs or affordable health care or decent housing. Too many kids grew up surrounded by violent crime, cycling through substandard schools where few had a shot to break out of poverty. And so like a body weakened already, undernourished already when the storm hit, there were no resources to fall back on."

In 2010, when Obama marked the five-year anniversary of Katrina in the second year of his presidency, he scarcely mentioned the issues of racial disparity that plagued the city, both before and after the storm, despite speaking at the historically black Xavier University in Gert Town.

Now in his second term, the President has become more open about addressing issues of race, including the opportunity gap visible in inner-cities around the country. On Thursday he carved out a moment to meet with young men participating in his My Brother's Keeper mentorship program, which seeks to bolster opportunities for African-American men and boys.

"As hard as rebuilding levees is, as hard as rebuilding housing is, real change -- real lasting structural change -- that's even harder," he said.

Book-ended by major events promoting his environmental agenda, Obama did not use the storm's anniversary to make another push to curb climate change, though he did convene a roundtable meeting to discuss steps to prevent the type of infrastructure collapse that devastated the Gulf Coast after Katrina hit.

Instead, he touted his administration's steady success in eliminating bureaucratic barriers to rebuilding New Orleans, and pointed to projects like an overhauled school system and newly rebuilt hospital as examples of a city on the upswing.

In the mostly African-American Lower Ninth Ward, where Obama spoke, the recovery efforts are varied: his venue was a multi-million dollar community center, built with the help of federal funds after Katrina, that sits only blocks from the abandoned cars and blighted lots that have become symbols of a slow recovery.

Just more than 50% of the neighborhood's housing units are now occupied, according to figures from the Data Center, which has tracked statistics in New Orleans in the aftermath of Katrina. The population in 2010 was just more than 2,000 -- 80% smaller than before the storm.

Photos: Anderson Cooper returns to New Orleans 10 years later Photos: Anderson Cooper returns to New Orleans 10 years later CNN's Anderson Cooper, covering Hurricane Katrina in New Orleans in 2005, reports on seeing a body on top of a car a week after the storm. Hide Caption 1 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Ten years later, Cooper returned to New Orleans and caught up with some of the people he met as he covered the disaster. Here, he revisits the spot where he saw the body and tells us who the man was. Hide Caption 2 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Laura Bane in 2005 speaks to Cooper in Waveland, Mississippi, after she lost her parents and her two brothers to the storm. Hide Caption 3 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Bane speaks to Cooper this year in Waveland about her memories of the storm. Hide Caption 4 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Shelton Alexander shares an emotional moment in 2005 after Katrina. He lost his home in St. Bernard Parish. Hide Caption 5 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Alexander in 2015 reflects on his experiences riding out the storm in the Superdome. He is now a poet and still lives in St. Bernard Parish. He is nicknamed "Shakespear"-- without the "e." Hide Caption 6 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Dr. Roderick Bennett was a third-year emergency room resident in 2005. He hoped to spend his entire career at Charity Hospital. Hide Caption 7 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later Bennett speaks with CNN in 2015 about his experiences. He now practices medicine in Florida, though he hopes to return to New Orleans one day. Hide Caption 8 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later In 2005, approximately 80% of New Orleans was under water after the levees breached. Hide Caption 9 of 10 Photos: Anderson Cooper returns to New Orleans 10 years later In 2015, there are still scars from the storm 10 years later, but much of the city has rebuilt and is thriving. Hide Caption 10 of 10

The average household income stands at $33,557 per year -- $4,000 less than it was in 2000, five years before the storm. Nearly one-third of the population lives below the poverty line, more than twice the national average.

"This recovery is at halftime," said Marc Morial, a New Orleans native who served as the city's mayor before becoming the president of the National Urban League. "And because it is at halftime, there is so much more to be done. Until Lower Nine is back, we cannot say this city is fully recovered."

In his remarks, Obama acknowledged the neighborhood's sometimes halting recovery, saying a speech in the Lower Ninth Ward might have "seemed unlikely" in the years immediately following Katrina but that forward-thinking residents had rallied together to reconstruct their neighborhood.

In some ways, Obama's language Thursday most closely echoes his remarks on Katrina from before he became President, including a 2007 speech wading into the racial disparities visible in the storm's aftermath.

Though he told a church crowd then that the administration of then-President George W. Bush was "colorblind in its incompetence" during its response to Katrina, he suggested the storm exposed long-festering inequalities in the city.

"Everyone here knows the disaster and the poverty happened long before that hurricane hit," Obama said then. "All the hurricane did was make bare what we ignore each and every day, which is that there are whole sets of communities that are impoverished, that don't have meaningful opportunity, that don't have hope and they are forgotten."