Many American cities and states showed signs last year of a slow recovery from the recession as median household incomes rose modestly and Americans were more willing to relocate to new communities, according to figures released Thursday by the Census Bureau.

In 2013, the Washington metro region once again had by far the highest median household income among the nation’s 25 largest areas, $90,000. Among all big metropolitan areas, only the San Jose region was higher, at about $91,500. Maryland had a higher income level than any other state, about $72,500. Virginia’s $63,000 was unchanged. The District’s income, $67,500, rose slightly.

Most places were still far below the peak in household incomes reached before the recession that began in late 2007. But many were off the lows reached as income levels continued to plummet after the recession officially ended two years later. Median household incomes in some large metro areas, including the Washington region, are approaching where they were when the recession ended. But other metro areas — particularly in Sun Belt cities such as Miami, Atlanta, Phoenix and Charlotte — have not bounced back to their 2009 levels.

“They’re still trying to recover from the huge morass they found themselves in as a result of the mortgage meltdown and the recession,” said William Frey, a demographer with the Brookings Institution. “Their economy was built on growth, in population and in jobs. And the merry-go-round just stopped.”

In an indicator that many Americans are feeling confident about their financial situation, more people moved last year to a new city or county than they had since 2007. Relocation essentially ground to a halt during the recession when people couldn’t get new jobs or sell houses that they were underwater on. The 17 million people who moved to a new county was up almost 3 percent in 2013. About 7 million of them moved long distance, a 7 percent gain since 2010.

Across the nation, income rise hints at recovery

Ken Johnson, a demographer with the University of New Hampshire, said states such as New York, Massachusetts and California are starting to lose residents again as people retire to warmer and cheaper places. And states such as Nevada, Arizona and Florida are gaining residents as new people arrive and fewer depart.

“Partially, it’s due to the improvement of the housing market, which means people can move if they want to,” he said. “During the recession, lots of people saw their retirement accounts were smaller than they had been, so they weren’t going to move. Now those accounts are worth at least as much, if not more. So people who stayed put are saying, ‘Let’s go ahead and move.’ ”

Many cities are experiencing modest growth and a gradual improvement in their budgets as housing markets and property tax revenue stabilize, said Christiana McFarland, director of research for the National League of Cities.

One factor holding down median household income in some places is that many of the jobs being created have high salaries or low wages, with little in between.

“In many of the states, there’s an immense amount of market polarization,” said Neil Bomberg, director for human development at the National League of Cities. “So the median begins to decrease, especially in states that have chosen not to increase the minimum wage.”

In cities and states where ­middle-income jobs are growing, much of the increase is because of local-government hiring among groups such as police officers and teachers, McFarland said.