Former Treasury Secretary Larry Summers has been saying for a while that the Federal Reserve shouldn't raise interest rates until its sees "the white of inflation's eyes," and he's sticking to that view.

The reason he feels that way: "the greater risks are on the side of [economic] slowdown and stagnation, rather than on the side of overheating and inflation," the Harvard professor tells CNBC.

That risk of a slowdown was reinforced by the March jobs report, which showed that non-farm payrolls rose only 126,000 last month, the weakest showing since December 2013.

Meanwhile, the personal consumption expenditures price index climbed just 0.3 percent in the 12 months through February, far below the Fed's 2 percent target.

"I look at what global bond markets are telling us. There is nowhere in the industrialized world where bond markets are looking for 2 percent inflation over the next decade. There is nowhere over the industrial world where they're looking for real interest rates, anything like 1 percent over the next decade. And that is telling us that an issue of a chronic excess of savings over investment is going to be importantly defining of our financial environment," he explains.

"If a defining reality is a tendency towards more savings over investment, that's something that economic policy has to adapt to. And rushing to raise rates would not be an appropriate adaptation."

There's no reason for the central bank to increase rates before inflation accelerates, Summers insists. "Pre-emptive wars don't work, and pre-emptive wars on inflation would be a big mistake."

Many Fed officials apparently agree with him. Minutes from the Fed's March policy meeting indicate that most of them want to wait until at least September before lifting rates.

The central bank has kept its federal funds rate target at a record low of zero to 0.25 percent since December 2008.

Meanwhile, former Fed Chairman Ben Bernanke addressed criticism of the central bank's massive easing program in his latest blog.

"Recently, opposition to accommodative monetary policy has coalesced around the argument that persistently low nominal interest rates create risks to financial stability, for example, by promoting bubbles in asset prices or stimulating excessive credit creation," Bernanke writes.

"Let there be no mistake: in light of our recent experience, threats to financial stability must be taken extremely seriously," the Brookings Institution economist explains.

"However, as a means of addressing those threats, monetary policy is far from ideal. First, it is a blunt tool. Because monetary policy has a broad impact on the economy and financial markets, attempts to use it to 'pop' an asset price bubble, for example, would likely have many unintended side effects."

Instead the Fed should use its financial regulatory and supervisory powers to maintain stability, Bernanke says. "Effective financial oversight is not perfect by any means, but it is probably the best tool we have for maintaining a stable financial system."

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