Novak Djokovic made light work of Damir Džumhur in round one ©Getty Images

Top seed Novak Djokovic breezed past Damir Džumhur to reach the second round of the US Open, while former women's champion Naomi Osaka is also into round two.

Serbia's Djokovic - a heavy favourite in the men's competition given the absences of Rafael Nadal and Roger Federer - needed less than two hours to beat Bosnian Džumhur 6-1, 6-4, 6-1.

Djokovic, who won the warm-up Cincinnati Masters also played in New York City, broke Džumhur's serve seven times in total.

Britain's Kyle Edmund awaits Djokovic in round two, following a four-set triumph over Alexander Bublik of Kazakhstan.

Victory at the US Open would move the Serbian to within two Grand Slam titles of Federer’s record of 20 and just one behind Nadal’s total of 19.

Djokovic is playing amid a backdrop of controversy, both over his conduct and comments regarding the coronavirus pandemic and a decision to leave the Association of Tennis Professionals Players Council to form a new players' association.

Chilean Cristian Garín was another seed to advance in the evening session, but needed five sets to do so.

The 13th seed fought back from two sets down to topple American Ulises Blanch 4-6, 5-7, 6-4, 6-4, 6-2.

Germany's Jan-Lennard Struff, seeded 28th, defeated Spaniard Pedro Martinez Portero in straight sets.

A potential third-round opponent for Djokovic, Struff will play Michael Mmoh of the United States next.

An all-Japanese clash between Osaka and Misaki Doi was the final match at Arthur Ashe Stadium.

Osaka - a winner here in 2018 - took the first set 6-2, but Doi fought back to claim the second 7-5 and set up a decider.

The number four seed's return game proved too strong for Doi, as Osaka broke twice to also win the final set 6-2 and advance to the second round, where Camila Giorgi of Italy awaits.

Osaka, who withdrew from the Cincinnati Masters final last week with a hamstring complaint, again used her platform to make a statement on racism and police brutality in the US, wearing a face mask that read "Breonna Taylor" as she entered the court.

Taylor was shot dead in her own home by Louisville Metro Police Department officers in March of this year.

Giorgi also needed three sets to shake off Belgian Alison Van Uytvanck.

Americans Alison Riske - seeded 13th - and Jennifer Brady - seeded 28th - also secured second-round places on the tournament's first evening. 

Riske defeated Tatjana Maria of Germany in 62 minutes, winning 6-3, 6-2, while Brady bettered Russian Anna Blinkova by the same scoreline.