New York, Sep 1 (IANS): Serbia's world No. 1 Novak Djokovic reached the second round of the US Open with a 6-1, 6-7(5), 6-2, 6-1 win over Holger Vitus Nodskov Rune in two hours and 15 minutes even as the Danish teen suffered from cramps in the final two sets at the Arthur Ashe Stadium.

Djokovic is now six match wins from becoming the first man since Rod Laver in 1969 to claim all four major titles in one season. The three-time US Open champion will next face Dutchman Tallon Griekspoor.

"It's tough to talk about (the) third and fourth sets because he barely moved (due to cramps). (From) my side, I started great. Played a really, really good first set. After that, I don't know, I was 4-3 serving in the second set. Everything was working well, but then I just lost the first serve," Djokovic said on Tuesday night.

"Credit to him for fighting. He had the crowd behind him. It was tough to play in my first match, even though I had tonnes of experience playing on this court, for him it was the first one," Djokovic told atptour.com.

"Still, you get nerves. You still are feeling a little bit rusty at the beginning. Obviously I'm pleased with the way I finished the match. Again, it was not a fair battle on the court with his unfortunate injury and cramping."

Entering the match, 18-year-old Rune had said, "I have a lot of belief in myself even though I'm up against the world No. 1." The Danish teen showed it by playing courageously in the second set and taking a tense tie-break, during which he rallied the New York fans on his side.

But ultimately, he was unable to sustain his aggressive play long enough to trouble the top seed further. Rune was visited by the trainer on multiple occasions in the final two sets to receive treatment on his upper legs for apparent cramping. Djokovic took advantage by hitting 55 winners to just 30 unforced errors.

"Unfortunately, my fitness let me down. I started cramping already in the beginning of the third set. From there on, it was tough," Rune said. "I knew if I (wanted) to win, I really had to fight for every point. With my body at this point, it was impossible."

After match point the 20-time major winner, who can pass Roger Federer and Rafael Nadal for most Slam titles with a trophy at the end of this fortnight, had a lengthy exchange with Rune at the net to give him encouragement.

"I just told him that he handled himself extremely well. He didn't want to stop," Djokovic said. "I thought he was going to stop (at) the end of the third. He just kept going with dignity, finished off the match. He deserved definitely my respect, the respect of a lot of people. He's still very, very young, 18 years old. He's got plenty of time ahead of him. I'm sure we're going to see a lot of him in the future."

Djokovic's next opponent, Tallon Griekspoor of the Netherlands, battled past big-hitting German Jan-Lennard Struff 2-6, 7-6(3), 4-6, 6-4, 7-5 after three hours and 38 minutes.

Djokovic is now 16-0 in first-round matches at the US Open. The Serbian has not lost in the opening round at a major since the 2006 Australian Open.