About 50 demonstrators gathered in Jackson Hole, Wyoming, holding signs reading "whose recovery is this" and "how many jobs do I have to work to be middle class?" Surrounded by the protesters, Nobel laureate economist Joseph Stiglitz also lent his voice, saying "this is not the time" to tighten policy.

"We are not algorithms in your computers. We are real people with real bills and real responsibilities," said Rod Adams, a protester who added that he makes $10.10 per hour.

The Fed's plans to abandon its yearslong near-zero interest rate policy have taken a turn recently amid stock market volatility fueled by concerns about the Chinese economy. The U.S central bank in recent months said it saw a strengthening labor market, describing job gains as "solid" after its July policy meeting.

Two former top Fed officials told CNBC that the central bank needs to evaluate how best to boost conditions for workers. Based on the last few years, easy policy may not necessarily fuel wage and job gains, noted former Philadelphia Fed President Charles Plosser.

"It's very important that we look beyond what's happening now and are looking to the long run," he told CNBC from Jackson Hole on Thursday.

While the central bank takes worker concerns "very seriously," it needs to evaluate how best to boost employment and wages, said Randall Kroszner, a former Fed governor. He added that it cannot base its decision on the fundamentals of another economy.

"You can't have Fed policy responding to every bump and wiggle that are coming out of the markets," he told CNBC from Jackson Hole.

He added that a rate liftoff in September of December of this year could make sense without a "negative downward shock" to inflation.