By Larry Fine

NEW YORK (Reuters) - Top seeds Novak Djokovic and Serena Williams face challenging early tests at the U.S. Open following Friday's draws for the year's last grand slam starting on Monday.

Djokovic, who has been bothered by a wrist injury, faces towering Jerzy Janowicz of Poland in his opening match at Flushing Meadows, and is likely to meet 48th-ranked Jiri Vesely of the Czech Republic in the second round.

Vesely beat the Serbian world number one earlier this season on clay in Monte Carlo.

"I'm doing everything in my power ... to make sure that I'm as close to 100 percent as possible," Djokovic told reporters, saying he hurt his wrist in Rio a few days before the start of the Olympic tournament, where he lost in the first round.

Williams, recovering from a shoulder injury that contributed to her third-round exit in Rio, drew Russian lefthander Ekaterina Makarova as her first opponent.

The 34-year-old American, seeking to break her tie with Steffi Graf for most grand slam singles titles in the Open era on 22, has a 4-1 career record against Makarova, but lost to the Russian in the fourth round at the 2012 Australian Open.

Williams is in a strong quarter that also includes fifth seed Simona Halep of Romania and 16th-seeded Australian Sam Stosur, who beat the American in the 2011 U.S. Open final.

Djokovic is seeded to face either Frenchman Richard Gasquet or big-serving American John Isner in the fourth round, with France's Jo-Wilfried Tsonga or 2014 champion Marin Cilic, who ended Andy Murray's win streak in the Cincinnati final, as possible quarter-final opponents.

Men's second seed Murray, who ran off 22 wins in a row including his second Wimbledon title and successful defense of his Olympics crown, appeared to get a more favorable draw.

The Scotsman opens against Czech Lukas Rosol, has Grigor Dimitrov of Bulgaria or Feliciano Lopez of Spain as potential fourth-round foes with Japan's sixth-seeded Kei Nishikori possibly waiting for him in the quarters.

Third seed Stan Wawrinka, who is in Murray's half of the draw, begins against Spanish veteran Fernando Verdasco, and may have to deal with a young Australian, Bernard Tomic or Nick Kyrgios, in the fourth round.

The dangerous Juan Martin del Potro of Argentina, the 2009 champion who showed in claiming Olympic silver that he is regaining form after a long recovery from an injured wrist, could be there to oppose the Swiss double slam winner in the quarter-finals.

Fourth-seeded Rafa Nadal, winner of 14 slams, and fifth seed Milos Raonic of Canada could clash in the quarters for a possible semi-finals showdown with Djokovic.

Rounding out the women's draw, second seed Angelique Kerber, who nearly unseated Williams as world number one but lost in the Cincinnati final, appears to have a comfortable early path.

Kerber, who opens against Polona Hercog of Slovenia, is seeded for a quarters clash against seventh seed Roberta Vinci of Italy, who shocked Williams in last year's Open semi-finals.

The German's potential semi-final opponent comes from a more impressive quarter that includes third-seeded French Open champion Garbine Muguruza, Olympic champion Monica Puig, Briton Johanna Konta and big-hitting American Madison Keys, the eighth seed.

In the other quarter in Serena's side of the draw, the leading seeds are Agnieszka Radwanska of Poland (4) and Venus Williams (6), who will aim for a semi-finals encounter with her sister.

(Editing by Andrew Both)