She also said officials would want to be confident that inflation was on track to head back up toward the Fed's 2 per cent goal before raising rates for the first time since 2006.
Labour Department data last week showed the jobless rate fell to a six-year low of 5.6 per cent even as hourly earnings dropped by 0.2 per cent in December from the prior month, the biggest comparable decline since records began in 2006.
Williams said the report shows "significant employment gains" are continuing in the US as it makes progress toward full employment, which he expects to reach by the end of this year or early in 2016.
"On the other side, the wage and price data are still soft, so in terms of thinking about June my views haven't really changed," Williams said. "If inflation data come in significantly softer than expected and we're not seeing some kind of better growth in wages, those are clearly factors that I'd be taking into consideration in the timing of liftoff."
The Fed's main gauge of prices, the personal consumption expenditures index, hasn't exceeded the central bank's 2 per cent objective since March 2012. It has slowed in recent months to a pace of 1.2 per cent in November from a year earlier.
The committee will meet this month in Washington. Fifteen of 17 officials have said they expect the federal funds rate will rise this year after remaining near zero since December 2008.
- Bloomberg