By Ann Saphir, Lindsay Dunsmuir and Jonnelle Marte

(Reuters) -Federal Reserve policymakers on Thursday sounded sanguine about the economic impact of the latest COVID-19 variant, but flagged rising inflation in remarks that suggested growing consensus for an earlier end to bond buys and, perhaps, earlier interest rate hikes next year.

Atlanta Fed President Raphael Bostic told the Reuters Next conference on Thursday it would be appropriate to end the central bank's bond-buying program by the end of March to allow the Fed to raise rates to deal with inflation.

The Fed, which began tapering its bond-buying last month at a pace that would end the program by June, is set to consider compressing that timeline when policymakers meet on Dec. 14 and 15.

With robust growth, an improving job market and inflation more than twice the Fed's 2% target, "I think having this finished some time before the end of the first quarter would be in our interest," Bostic said.

And if inflation continues as high as 4% through next year, as some forecasters project, "there’s going to be a good case to be made that we should be pulling forward more interest rate increases and perhaps even do more than the one I’ve penciled in."

Only half of Fed policymakers in September thought the Fed should start raising rates next year, with the rest expecting the first rate hike in 2023. Since then, several appear to have moved their rate hike expectations earlier.

After this week's hawkish Fed commentary, rate futures traders now see the first Fed rate hike in May.

Though the new Omicron variant's severity and transmissibility will determine how afraid people are, Bostic said each successive wave of COVID-19 has led to milder economic slowdowns. If that holds, the economy will continue to grow through it, he said.

Bostic is hardly the Fed's lone hawkish voice. Earlier this week, Fed Chair Jerome Powell said he wants a faster taper timeline on the table at this month's meeting.

Bostic said he doesn't see "tension" between the Fed's two goals of price stability and full employment at the moment. Once the Fed does start raising rates, he said, it will likely do so at a "slow and steady" pace. Though if inflation does not recede as expected over the next year or two, it may need to "take more strident steps" to rein it in, he said.

But other Fed policymakers appear increasingly worried they may need to put the brakes on growth before the labor market has fully healed and millions of unemployed Americans find jobs.