By Steve Ginsburg

NEW YORK (Reuters) - Second seed Rafael Nadal reached his first U.S. Open quarter-final on Monday and the Spaniard is showing no signs that he intends to stop there.

Hoping to close the gap with world number one Roger Federer, the left-hander has lost just one set in four matches, including Monday's 6-1 7-6 6-4 fourth-round triumph over Jiri Novak.

Nadal, at 20 already a double French Open champion, is playing down his results at this year's Open so far.

"I am happy. I am playing my best tennis here since last month, that's for sure. I'm not playing the tournament of my life, but I am not playing bad."

With Federer having won the Open for the last two years, Nadal conceded: "It is important for me play good here".

Second seed Justine Henin-Hardenne, seeking her second U.S. Open crown, breezed past Israel's Shahar Peer 6-1 6-0 in just 50 minutes, while number four seed Elena Dementieva booked a spot in the last eight by beating France's Aravane Rezai 7-5 6-4.

Former Open champion and 10th seed Lindsay Davenport blasted 35 winners to oust seventh seed Patty Schnyder of Switzerland 6-4 6-4 in her fourth-round match.

UNFORCED ERRORS

On the men's side, just one day after sending the great Andre Agassi into retirement, 112th ranked Benjamin Becker of Germany committed 39 unforced errors as he was eliminated 6-3 6-4 6-3 by ninth seed Andy Roddick.

Although Novak lost to Nadal in just over two hours, he was satisfied with his play in the second and third sets at least.

"In the first set, I was just trying to get my rhythm," the Czech said. "In the beginning of the second set I improved my game a lot. But he was definitely better."

While Nadal is almost unbeatable on the slow red clay of Roland Garros, Novak believes the Spaniard could walk away with his first title on the hardcourts at Flushing Meadows.

"His game is excellent, on the hardcourt as well," said Novak. "He's won so many tournaments on the hardcourt already. He can beat any player in the world.

"He's improved a lot on the fast court. Did you see Wimbledon where he reached the final on the grass court? Nobody expected it but he did it."

At 30 years old, Davenport may be reaching the end of the road at the Open, a tournament she won in 1998. Next up in the quarters is five times grand slam champion Henin-Hardenne.

The Belgian holds a 6-5 career lead over Davenport but more telling is that she has a six-match winning streak against the American.

"I played her a lot at the beginning of her career and I think over the years she's improved her forehand, her confidence," said Davenport. "So she's kind of a different player.

"I've watched her a play lot this year... and also last year, her strengths, her weaknesses. For me, there's no question I have to keep the balls coming back at her hard and deep and not give her a lot of time to set up and use her forehand."