By Simon Cambers

NEW YORK (Reuters) - Britain's Andy Murray had less trouble reaching round three at the U.S. Open on Wednesday than he has this week avoiding the New York paparazzi, who have been hanging on the Olympic champion's every word.

The Scot stepped up a gear from his first-round match as he crushed world number 117 Ivan Dodig of Croatia 6-2 6-1 6-3 under the lights at Flushing Meadows.

Since he won the gold medal at the London Olympics earlier this month, Murray has found himself centre of attention wherever he goes, including in New York.

"There have been a few people hanging around outside my hotel," Murray said in a courtside interview.

"They asked me if I had seen the photographs of Prince Harry," referring to the pictures in British tabloid newspapers of a naked Prince Harry in a Las Vegas hotel.

"I said 'no comment'," Murray laughed.

"Another one asked me what I thought about the Crown Jewels. It's a little bit different to what I'm used to but it's alright."

Dodig can boast wins over Rafa Nadal and Jo-Wilfried Tsonga but he was blown away by a rampant Murray, who raised his game from a scratchy opening-round display under the watchful eye of coach Ivan Lendl.

"I thought I played well," Murray said. "There were a lot of long rallies and he moves extremely well. I moved my feet very well tonight and I played well."

The Scot broke in the third game of the match and never looked back as he clinched a meeting with the winner of the all-Spanish battle between 30th seed Feliciano Lopez and Pablo Andujar.

Murray will now have two days off before his next match on Saturday but said the chance of him enjoying a bit of time off before then were somewhere between slim and none.

"With the coach I have, I'm sure I'll be back on the practice court tomorrow," he laughed. "I'll try to do something tomorrow night."

(Editing by Nick Mulvenney)