That seeming paradox — a steadily improving economy with faster job growth even as millions of potential workers remain stuck on the sidelines — is among the biggest challenges now facing politicians in Washington and policy makers at the Federal Reserve.

The latest numbers highlight the problem. The unemployment rate remained flat last month at 6.3 percent, the lowest since September of 2008. But the portion of the population in the work force did not budge either, remaining stuck at 62.8 percent, a depressed level last seen in the late 1970s. Although retiring baby boomers are responsible for some of the decline in participation in recent years, most experts say they believe a substantial amount is because people are giving up the search for a job entirely and dropping out of the work force.

“We’ve gotten the unemployment rate down,” said Byron Wien, vice chairman of Blackstone Advisory Partners and a Wall Street strategist for decades. “But are we really creating enough jobs to bring people back into the work force? We’re not and we need to create more. We’re still a long way from where we need to be.”

The varying fates of workers in the recovery was also evident from the data on joblessness by educational level. While unemployment among college graduates dropped by 0.1 percent, to 3.2 percent in May, it increased by 0.2 percent, to 9.1 percent for high school dropouts, and by 0.2 percent, to 6.5 percent for workers with only a high school diploma.

Still, experts said that the report was strong enough to keep the Fed on its current trajectory of gradually reducing monthly bond purchases aimed at stimulating the economy, while avoiding the danger that an improving labor market will create upward pressure on inflation, always a worry for central bankers. For example, average hourly earnings rose by 5 cents, to $24.38, in May, the Labor Department said, and are up 2.1 percent in the last 12 months, not much more than underlying rate of inflation.