* US service sector sags in June as orders sink

* US weekly jobless claims rise labor market slows

* Dollar hits two-week low

* U.S. non-farm payrolls report due on Friday

July 3 (Reuters) -

Gold prices rose more than 1% to a near two-week high on Wednesday, driven by increased bets for a September interest rate cut by the Federal Reserve after recent U.S. data suggested that the labor market was softening.

Spot gold was up 1.4% at $2,362.32 per ounce by 10:09 a.m. ET (1409 GMT). U.S. gold futures climbed 1.7% to $2,372.40.

"The precious metals complex, as well as base metals, are rallying across the board on ADP and jobless claims data that reinforces the 'softening economy' narrative which will likely lead to the first rate cut in September," said Tai Wong, a New York-based independent metals trader.

"Bulls are trying to get ahead of what many believe will finally be a weak payrolls report on Friday," he added.

First-time applications for U.S. unemployment benefits increased last week, while the number of people on jobless rolls rose further to a 2-1/2 year high towards the end of June, consistent with a gradual cooling in the labor market.

A measure of U.S. services sector activity

slumped

to a four-year low in June amid a sharp drop in orders, potentially hinting at a loss of momentum in the economy at the end of the second quarter.

Following the U.S. data, the dollar slipped to a two-week low, making gold more attractive for other currency holders, while the yield on the benchmark U.S. 10-year Treasury note slid. [USD/

The market now sees a 68% chance of the Fed cutting interest rates in September as well as another cut in December. Lower rates reduce the opportunity cost of holding non-yielding bullion.

Investors now look forward to the minutes from the U.S. central bank's latest policy meeting due later in the day, and the non-farm payrolls report due on Friday for more clarity on U.S. rate cuts.

Elsewhere, spot silver rose 3.4% to $30.52 per ounce, platinum gained 1.8% to $1,008.50 and palladium climbed 2.7% to $1,049. (Reporting by Brijesh Patel in Bengaluru; Editing by Anil D'Silva)