The U.S. services sector grew modestly for a second month in a row in October and private sector employers cut jobs at the slowest pace in more than a year, adding to signs the economy is crawling back to health.

The Federal Reserve -- the U.S. central bank -- at the end of a two-day policy-setting meeting on Wednesday nodded to improving economic data but said it would still keep borrowing costs near zero for an extended period as recovery will likely be sluggish.

The weak U.S. economy is having political repercussions. Voters voicing fears about the economy elected Republicans in state governor races in Virginia and New Jersey on Tuesday, in contests that analysts said served as a warning shot to Democrats looking ahead to 2010 voting.

The services sector, which represents about 80 percent of U.S. economic activity, grew in October, but the growth was less than forecast and the survey's employment index disappointed analysts.

On balance, the non-manufacturing survey suggests that economic growth is continuing at a moderate pace, but that the labor market is still in rough shape, JPMorgan Chase analysts wrote in a note to clients.

The Institute for Supply Management's U.S. services data followed European surveys showing service sector activity expanded at its fastest in 22 months in October in the euro zone, and in Britain at its briskest since August 2007, when the global credit crunch struck.

The ISM services index slipped to 50.6 last month from 50.9 in September, below economists' median forecast for a rise to 51.5. A reading above 50 indicates growth. The employment index fell to 41.1 in October from 44.3 in September.

A separate report showed that while companies are still cutting jobs, they are doing so at a slower pace.

The private sector jobs report by ADP Employer Services LLC showed companies cut 203,000 jobs in October, fewer than the revised 227,000 in September and the lowest since July 2008.

There are still a lot of people out there feeling pain ... but we are heading in the right direction, said Macroeconomic Advisers' chairman Joel Prakken.

The ADP report is seen by many analysts as a proxy for the government's closely-watched monthly report on nonfarm payrolls, which will be released on Friday.

Analysts polled by Reuters expect Friday's employment report to show U.S. payrolls shrank by 175,000 and the unemployment rate hit a new 26-year high of 9.9 percent in October.

We did have month-on-month improvement in the ADP report, but we are still losing jobs, and the 10 percent unemployment barrier has huge psychological significance, said Michael Woolfolk, senior currency analyst at BNY Mellon in New York.

There were other glimmers of hope on Wednesday for the labor market's outlook. A report by global outplacement consultancy Challenger, Gray & Christmas showed planned layoffs by U.S. companies in October slowed for a third consecutive month to a 19-month low.

There were also some positive signs from the U.S. housing market. Mortgage applications rose for the first time in four weeks, reflecting a jump in demand for home refinancing loans as interest rates on 30-year loans dropped below 5 percent, data from an industry group showed.

The Mortgage Bankers Association said rates on 30-year fixed-rate mortgages, the most widely used loan, fell below 5 percent for the first time in four weeks. The 5 percent level is something of a psychological tipping point, typically sparking home loan refinancing activity.

(Additional reporting by Chris Reese, Richard Leong, Julie Haviv and Camille Drummond in New York and Mark Felsenthal in Washington; Editing by James Dalgleish)