WASHINGTON  - The pace of job losses slowed in many U.S. states in October, and the unemployment rate slipped in hard-hit Michigan, the Labor Department said on Friday, hinting the recession may be easing in some areas.

Michigan's jobless rate fell to 15.1 percent in October from 15.3 percent in September, although it remains the highest in the United States.

The rate in Nevada, the second-highest, dipped to 13 percent from 13.3 percent. Rhode Island was close behind at 12.9 percent, followed by California at 12.5 percent.

Alaska and Wyoming had the largest increases in their unemployment rates over the month, as changes in the energy sector hit the oil and natural gas rich states.

North Dakota continued to have the lowest unemployment rate in the nation at 4.2 percent, up from 4.1 percent the previous month. Nebraska had the second lowest at 4.9 percent, followed by South Dakota at 5 percent.

Speaking at an event at Brookings Institution in Washington, D.C. on Thursday, Steve Cochrane from Moody's Economy.com said the first states to recover from recession will be in the middle section of the country.

Currently, 15 states and the territory of Puerto Rico have over 10 percent unemployment. One of those states, Illinois, has a rate of 11 percent, its highest since August 1983.

The slowing pace of job loss and other leading economic indicators bring with it cautious optimism, said Illinois Department of Employment Security Director Maureen O'Donnell.

The national unemployment rate for October was 10.2 percent, the highest since April 1983.

Nonfarm payroll employment increased in 28 states and the District of Columbia during October and stayed the same in one state, the Labor Department said.

Texas had the largest increase of 41,700 jobs, followed by Michigan, with 38,600, and California, with 25,700.

Michigan had the largest monthly change -- of 1 percent.

Since July, professional and business sector jobs in the state have increased because of privatization of education-related work, according to the Michigan employment department. The state also had gains in October in education, construction and manufacturing, which has increased for four straight months.

The department said the state's unemployment rate and number of jobs have been stabilizing since the summer, when the federal government's car-buying program known as Cash for Clunkers propped up demand for cars made in the state.

Many economists say the longest economic downturn in the United States in decades likely ended in the last few months, and states are eager to determine whether they too hit bottom.

Unemployment rates are the best gauge of recovery in states' financial health as job losses cause state tax revenues to fall and social service costs to rise.

On the positive side, South Carolina gained 1,100 jobs in October, according to the State Employment Security Commission.

The gain was small when compared to the 60,500 positions it lost from the previous October and the 95,000 jobs it lost since December 2007, when the recession began, according to the commission's statistics.

(Reporting by Lisa Lambert; Editing by Andrew Hay)