By Colleen Jenkins

(Reuters) - Republicans increased their majority of U.S. governors' offices on Tuesday after voters in North Carolina chose their first Republican state chief executive in 20 years.

In the swing state of New Hampshire, former state Senate majority leader Maggie Hassan won the gubernatorial election, keeping the seat in the Democratic column, ABC said.

Incumbent Democratic governors in Missouri, West Virginia, Vermont and Delaware won re-election, according to TV news projections. North Dakota voters re-elected Republican Governor Jack Dalrymple, the Associated Press said.

In Indiana, where Republican Governor Mitch Daniels is stepping down due to a term limit, Republican Mike Pence picked up the victory, Fox News reported.

Eleven governorships were in play on Tuesday, though only a handful of races were considered competitive and all were overshadowed by the White House and congressional contests.

Democrats were on the defensive with four of their party's incumbent governors stepping down compared with just one Republican. Democrats battled to keep control of governorships in tough races in New Hampshire, Montana and Washington, which like North Carolina have outgoing Democratic governors.

In North Carolina, former Charlotte mayor Pat McCrory notched a decisive victory over his Democratic challenger, Lieutenant Governor Walter Dalton, who conceded.

McCrory had maintained a consistent lead over Dalton during the race after losing to Governor Bev Perdue by a slim margin in 2008.

Perdue, the state's first female governor, decided not to seek a second term amid declining popularity.

In Washington, former Democratic congressman Jay Inslee and Republican state Attorney General Rob McKenna are in a tight race that may not be decided for several days due to the time it takes to count ballots in a state where everyone votes by mail.

Incumbent Governor Christine Gregoire, a Democrat who is retiring after two terms, won by just a handful of votes after multiple recounts and legal battles in 2004, and this year's contest could be similarly tight.

The Republican incumbent governor in Utah is expected to prevail.

(Reporting by Colleen Jenkins in Richmond, Virginia; Additional reporting by Jonathan Weber in San Francisco; Editing by Leslie Gevirtz)