S&P 500 
In an interview with Reuters, Williams estimated the Federal Reserve would continue trimming its bond portfolio well into next year. He also said he felt rates had reached his current view of a lower "neutral" level, with growth and unemployment levelling off and inflation, if anything, a bit weaker than hoped.
Asked if it would take some sort of shock to resume rate increases, he said it would require one or more of those factors to surprise to the upside.
"I don't think that it would take a big change, but it would be a different outlook either for growth or inflation" to return to hiking rates, Williams, one of the Fed's three vice chairs and a key voice on rate policy, told Reuters.
Williams' comments, made just weeks after the U.S. central bank paused its once quarterly rate hikes, underscore just how high the bar would be for tighter monetary policy, and suggest that such a move may not come anytime soon.
The Fed could also keep levels of bank reserves on its books that are far closer to current levels than previously thought, Williams said.
Along with its rate-hike holiday, Fed policymakers are finalising plans on how they would end the reduction of their balance sheet, which includes holdings of bank reserves bulked up in part by the Fed's need for cash to buy bonds to halt the global financial crisis a decade ago.
Williams estimated the so-called balance sheet roll off could end when bank reserves get to "maybe $1 trillion of reserves or somewhat more than that," about $600 billion (459 billion pounds) less than current levels.
The figure is "a guess today of the amount of reserves that will be held in the system in the future - but again we are learning and will get a finer touch on that," he said.
That view implies the runoff would continue at least into next year at its current pace. At least two Fed policymakers have said the Fed could stop making changes to the portfolio this year.
Williams, who is vice chairman of the rate-setting Federal Open Market Committee and votes when that group meets, said policymakers are "in a very good place," with rates around neutral, the U.S. economy growing and price pressures subdued.
"Monetary policy is where it should be," he said. "It's around my view of what neutral interest rates are."
After Williams' remarks, stocks pared gains into the market close Tuesday afternoon, with the S&P 500 ending up 0.15 percent. Yields on U.S. Treasury bonds fell. Benchmark 10-year notes fell to 2.64 percent from a high near 2.68 percent earlier in the day.
After its most recent meeting, Fed policymakers signalled their three-year drive to tighten monetary policy may be at an end due to a cloudy U.S. and global economic outlook as well as impasses over trade and government budget negotiations. Further details on the policy meeting at the end of January are expected when the Fed releases records from its deliberations on Wednesday.
The Fed increased interest rates three times in 2017 and four times last year, pushing them up to between 2.25 percent and 2.5 percent at its final 2018 meeting in December.
The central bank's balance sheet ballooned to over $4 trillion in the wake of the 2007-09 recession but policymakers began trimming bond holdings in the final months of 2017.
(Reporting by Howard Schneider, Jonathan Spicer and Trevor Hunnicutt in New York; Editing by Chizu Nomiyama and James Dalgleish)
By Howard Schneider, Jonathan Spicer and Trevor Hunnicutt
