Aug 6 (Reuters) - Federal Reserve Bank of St. Louis President Alberto Musalem said on Thursday it is critical for monetary policy to keep working to bring down inflation pressures amid ongoing risks to the central bank's price-pressure mandate, and should not be set to bolster high productivity levels in hopes of lower future inflation. 

"Inflation is well above the (Federal Open Market Committee's) 2% target, and the balance of risks is tilted toward inflation remaining above target a year or more from now," Musalem said in the text of a speech prepared for delivery in São Paulo, Brazil.

"It is crucial that monetary policy put a meaningful restraint on underlying inflation, rather than tolerating somewhat higher inflation today to pursue productivity growth tomorrow," he said.

Musalem dedicated the bulk of his remarks to examining a potential trade-off whereby the Fed keeps policy easier than it otherwise would be to help allow for higher rates of productivity, hoping that over the longer run this will lead to lower price pressures.

He said such a move would be a mistake.

"The trouble is that this reasoning takes the central bank's credibility for granted," the official said, adding,  "the bargain only works because households, firms and investors keep expecting inflation to return to target."

However, "a central bank seen to tolerate above-target inflation on the promise of a future productivity windfall can put that anchor at risk," Musalem said.

He also said that the economy has been "resilient" over recent months, while noting "the labor market has stabilized with solid payroll growth and an unemployment rate close to its longer-run value."

Musalem's remarks were his first since last week's Federal Open Market Committee meeting, where officials kept their interest rate target range steady at between 3.5% and 3.75% amid ongoing expectations in markets officials will have to lift rates at some point to bring down high levels of inflation.