As President Trump rails against the Federal Reserve and urges it to lower interest rates, a similar push is coming from a group founded this year by three left-leaning millennials — albeit for very different reasons.

Mr. Trump regularly points out that inflation is low and says that the Fed should slash rates, which would weaken the dollar and help with his continuing trade wars. The new group, Employ America, wants central bankers to place a higher priority on fostering job growth and sees looser monetary policy as a way to protect workers as the economy shows early signs of slowing. It is using research, and Twitter, to make its case.

The campaign may seem oddly timed: Unemployment in the United States is at a nearly 50-year low, and there are more job openings than applicants. The Fed’s key benchmark interest is also low, relative to past business cycles.

But Employ America is embracing an unusual moment in the politics of central banking. Democrats have long favored lowering interest rates to fuel stronger growth even if doing so risked raising prices, while Republicans have traditionally criticized such moves as potentially inflationary.