(Reuters) - As the Federal Reserve's policy-setting committee wraps up its third meeting of the year, a critical task awaits the U.S. central bank: narrowing the wide gap between how it and the markets view the path of interest rates.

The Fed previously ruled out raising rates at the end of its two-day meeting on Wednesday, and the chances of a hike at the June meeting, while still on the table, have steadily decreased amid a drum-beat of weak first-quarter economic data.

The central bank says its decision on when to raise rates will be data-dependent and made on a meeting-by-meeting basis, a stance that it may reaffirm on Wednesday.

Economists say September is more likely than June for the Fed's so-called "lift-off." It has kept rates near zero since late 2008 as part of its effort to spur the recovery from the financial crisis.

Futures traders see an even later time horizon, meaning they have little trust in the Fed's message that it's moving ahead with plans for what would be the first rate hike since June 2006.

The Fed faces a dilemma this week, according to Bank of America: accommodate market expectations of a later lift-off, or "update their communications to nudge the market in the Fed's direction." Bank of America's rates and currencies team said on Monday it expects the Fed to lean more to the latter option.

Futures traders put the odds of a September hike at only 25 percent, according to CME Group's FedWatch. The Fed's median federal funds rate estimate in December is 0.625 percent, nearly double where futures contracts show the rate that month.

The Fed could nudge investors on Wednesday by striking a more hawkish tone on inflation.

Stubbornly low inflation has been among the factors holding back the Fed's lift-off plans, but U.S. consumer prices ticked higher for a second straight month in March due in part to a rebound in energy prices.

Fed officials say the factors behind low inflation - a drop in the cost of oil and a rising U.S. dollar - are transitory, and believe prices will rise once those swings level off.

"A September lift-off is the marginal favorite, but June and July are possibilities if it becomes clear quickly that the first-quarter slowdown was a temporary weather-related blip rather than something more serious," Capital Economics said in a research note on Monday.

Employers added just 126,000 workers last month, the fewest since December 2013, breaking a 12-month streak of gains above 200,000. Manufacturing, housing and consumer spending data also have pointed to weakness.

The U.S. Commerce Department is scheduled to issue its first snapshot of first-quarter GDP at 8:30 a.m. EDT (1230 GMT) on Wednesday, with economists polled by Reuters expecting an anemic 1 percent annual rate of growth.

At the core of the Fed's struggle is whether to view the inflation rebound as a key step forward, or to view the overall economic data as a sign the markets are not yet ready to have the monetary policy stimulus punch bowl taken away.

JP Morgan predicted in a note last week that the meeting will be "relatively uneventful" and that the third paragraph in the Fed's policy statement, where it gives its rate guidance, would remain mostly the same as March, when the central bank said lift-off was dependent on further improvement in the labor market and "reasonable confidence that inflation will move back toward 2 percent over the medium-term."