Former Treasury Secretary Lawrence Summers say the Fed can pull off a soft landing, but warns that it would be a "big mistake" to think that the economy is "out of the woods".

In an interview on CNN's "Fareed Zakaria GPS" Summers said it "looks more possible that we'll have a soft landing than it did a few months ago."

While cautioning about the inflation indicators, Summers said, "They're still unimaginably high from the perspective of two or three years ago, and that getting the rest of the way back to target inflation may still prove to be quite difficult,"

On Friday, the Labor Department reported blowout jobs market numbers for January. The U.S. added 517,000 jobs last month, well above average economist estimates of 187,000 jobs.

The unemployment rate was 3.4%, below economist estimates of 3.6%. And the Wages were up 4.4% year-over-year and increased 0.3% from December.

The Fed hiked interest rates by 25 basis points last week, bringing its target fed funds rate up to a range of 4.5% to 4.75%.

Summer's was asked if triggering a recession was worth it to bring down inflation, and if a 3 to 3.5% inflation rate could become the norm, Summers said it comes down to a trade-off between short-term reductions in unemployment and permanent changes in inflation.

The benefit we can get from pushing unemployment low is, on almost all economic theories, likely not to be a permanent one," Summers said. "But if we push inflation up and those inflation expectations become entrenched, we're going to live with that inflation for a long time."

Last month, he told Bloomberg that it's a good sign inflation is starting to cool down, even as the job market remains resilient.

I'm still cautious, but with a little more hope than before. Soft landings are the triumph of hope over experience, but sometimes hope does triumph over experience," Summers said.