CORRECTED - UPDATE 3-U.S. airline in-flight security rules eased-TSA

(Corrects final paragraph to show spokeswoman is from TSA, not JetBlue)

* TSA says it updated in-flight security rules

* Will let pilots determine whether to enforce them (Recasts to show TSA confirming the news, adds details about JetBlue resuming LiveTV service; adds Washington DC dateline)

CHICAGO/WASHINGTON, Dec 28 (Reuters) - The U.S. Transportation Security Administration (TSA) will now give air captains discretion over when commercial airline passengers can move about the cabin and what they can have on their laps.

The update of airline security rules follows what U.S. government authorities called a thwarted attempt by an individual on Christmas day to blow up a Northwest Airlines flight as it approached Detroit from Amsterdam.

President Barack Obama said that as a result of this oversight, he had ordered a thorough review of the screening process.

The TSA confirmed that pilots can now decide whether to allow passengers to keep items in their laps or require them to be seated during portions of the flight.

The agency also will let pilots and airlines determine whether in-flight entertainment systems that show a plane's location should be turned off to avoid a security risk, a source with direct knowledge of the rules said earlier Monday.

JetBlue Airways (JBLU.O) announced through its Twitter page earlier Monday that its LiveTV service resumed on its flights.

"TSA will continuously review and update these measures to ensure the highest levels of security," said TSA spokeswoman Kristin Lee.

(Reporting by Kyle Peterson in Chicago and Jeremy Pelofsky in Washington; added reporting by Deepa Seetharaman in New York; Editing by Leslie Gevirtz, Steve Orlofsky and Bernard Orr)