By Deepti Govind and Sweta Singh

(Reuters) - The Federal Reserve is likely to raise U.S. interest rates in September and possibly as soon as July, according to a Reuters poll taken in the days after news of a sharp drop in hiring that has led some to worry that the economy is losing momentum.

Fed watchers surveyed by Reuters this week saw a median 40 percent chance of a hike in July and a roughly two-in-three chance of a September move, which would extend to nine months the time that has elapsed since the first hike in December.

About four-fifths of the 92 economists surveyed said the Fed will raise rates at either the July or September meetings.

Markets are not fully pricing in an increase until December, though commentary from Fed officials in recent weeks suggests that they are keen to raise sooner rather than later.

"If the Fed does not raise rates during the summer, in response to current indications of rising inflation, it will probably be because a global financial crisis has supervened," wrote Stephen Lewis at brokerage ADM ISI.

"In those circumstances, the odds are against the crisis subsiding far enough to give the Fed much chance to tighten in the remainder of the year."

Polls show a tight race ahead of a June 23 referendum in Britain over whether to remain in the European Union. This, along with the U.S. hiring slowdown, has created enough concern to push the likelihood of a rate hike at the June 14-15 meeting almost completely off the table.

Should Britain choose to remain, financial markets ought to avoid another bout of turmoil and if U.S. payrolls bounce back from a dismal 38,000 in May, a Fed rate rise that officials have been talking up will likely come back into focus.

"The longer they wait, the more data they have. If their view is playing out that the economy is on a better footing than suggested by the last payroll report, I think they'd become more likely to hike," said Daniel Silver, economist at JP Morgan.

"We think May is going to prove to be an outlier in terms of job growth and we're going to see some pickup in the coming months, but I think the Fed wants to see that really before hiking."

The unemployment rate has fallen to 4.7 percent, close to what many economists and Fed officials would call full employment - and, therefore, close to meeting one of the two parts of the central bank's dual mandate.

"Job growth is slowing and it should be slowing because we've basically reached full employment," said Michael Gregory, head of U.S. economics at BMO Capital Markets.

On the inflation front, core personal consumption expenditures inflation, the measure the Fed prefers, is running at 1.6 percent, not far below the Fed's 2 percent target.

Forecasters in the poll expect core PCE inflation to continue to creep higher and average 1.7 percent this year and 1.8 percent next, unchanged from last month's consensus, suggesting they are more or less in line with the Fed's latest projections.

Economic growth is expected to bounce back after a subdued first quarter, as it has in the recent past. Median forecasts put growth at an annualized 2.3 percent in the second quarter, and 2.4 percent in the third and fourth quarters.

But economic growth has not been that stable throughout the several years of recovery from the financial crisis.

(Polling by Kailash Bathija, Shrutee Sarkar and Vartika Sahu; Analysis by Krishna Eluri; Editing by Ross Finley)