* Dollar index bounces off one-month lows

* Euro under renewed pressure, sterling continues to drift lower

* Risk sentiment sours

By Ian Chua

SYDNEY, June 10 (Reuters) - The dollar clung to modest gains early on Friday, having bounced off one-month lows as the euro took a heavy spill while sterling stayed under a cloud on jitters over the upcoming Brexit vote.

The dollar index stood at 94.130, pulling away from a trough near 93.400. Driving the index's rise was a bearish turn in the euro, which slid to $1.1316 from a one-month high of $1.1416.

A Reuters report on Commerzbank looking to put billions of euros in vaults rather than pay a penalty charge for parking them with the European Central Bank appeared to have unsettled an already nervous market.

"It seems the news made waves early in the European session Thursday, our London team reporting that this was credited for the euro being sold across the board," analysts at National Australia Bank wrote in a note to clients.

The common currency also plumbed a fresh three-year low of 120.315 yen but has since drifted up to 121.075.

The market continued to give sterling a wide berth, pushing the currency to $1.4464, well off this week's peak of $1.4664.

The pound was back near the bottom of a $1.4350-$1.4750 range, just two weeks out before Britons vote in the referendum on EU membership.

BlackRock, the world's largest asset manager, said financial markets may be under pricing the risk of Britain leaving the EU.

With the euro zone and the UK in focus overnight, the dollar enjoyed a small reprieve. Dollar bulls had been hit hard since last Friday's disappointing payrolls data convinced investors that the Federal Reserve will not hike rates at next week's policy review.

A fresh batch of U.S. data on Thursday was more encouraging with a surge in wholesale inventories in April prompting economists to lift their second-quarter economic growth estimates.

A stand out performer was the New Zealand dollar, which staged a broad rally after the Reserve Bank of New Zealand on Thursday skipped a chance to cut interest rates and appeared reluctant to cut again.

The kiwi powered to a one-year high just shy of 71.5 U.S. cents and was last at $0.7116.

There is little on offer for Friday, but China's industrial production and retail sales due on Monday will set the tone for next week.

(Reporting by Ian Chua; Editing by Eric Meijer)