No need for near-zero Fed rates anymore: Experts

The strong May jobs report shows the U.S. economy is ready for a tighter monetary policy, two experts said Monday.

On Friday, the Labor Department said the U.S. economy added 280,000 jobs last month, well-above the estimated 225,000. The unemployment rate rose by 0.1 percent to 5.5 percent. In another recent report, the government said the economy contracted 0.7 percent during the first quarter.

"I'm glad this makes everyone feel better about the second quarter, and I agree … that September is the most likely time [for higher rates]," Michelle Girard, chief U.S. economist at the Royal Bank of Scotland, said on CNBC's "Squawk Box." "We are no longer in an emergency situation that requires the emergency-level [rates] we're sitting at right now.

Michael Ryan, chief investment strategist at UBS, agreed with Girard's assessment.

Read More Nonfarm payrolls total 280,000; unemployment rate at 5.5%

"I think we've gotten to the point where we've seen some healing in terms of structural damage that was done after the financial crisis," he said on Squawk Box." "We're seeing more evidence that the inflationary risks are going to abate. This is the environment we see when we have the economy gaining some traction."