Naomi Osaka has the hopes of the entire host nation resting on her.

Novak Djokovic is attempting to accomplish something that no man has done before in tennis.

Both players are after something special at the Tokyo Olympics, and both produced convincing victories Monday to reach the last 16 at Ariake Tennis Park.

Osaka crushed winners off both wings -- forehand and backhand -- seemingly at will in a 6-3, 6-2 victory over 49th-ranked Viktorija Golubic of Switzerland. Then Djokovic dispatched 48th-ranked Jan-Lennard Struff of Germany 6-4, 6-3.

"There's a lot of attention towards tennis as a sport in this Olympic Games," Djokovic said. "We are grateful, because we are representing our country, ourselves, but also our sport in the Olympic Village."

Despite this being her first tournament back from a two-month mental health break, Osaka's strong start is hardly a surprise considering that the Olympic tournament is being played on hard courts -- the surface on which she has won all four of her Grand Slam titles.

It was similar to the way Osaka overwhelmed Saisai Zheng of China a day earlier, and it extended her momentum after carrying out the ultimate honor at the Games' opening ceremony by lighting the Olympic cauldron.

The Japanese superstar, who grew up in the United States, was asked in March to handle the flame honors but said she "didn't feel pressure" about the assignment.

"I felt more excitement," Osaka said. "It was like a sense of duty, like something I wanted to accomplish.

"It's something that you see as a kid on TV. You gather around the TV with your family at the Olympics and you watch the whole ceremony," Osaka added. "I know my grandparents were probably crying, and my mom, of course."

If Djokovic can win four more matches, he'll not only have won his first Olympic title, he'll also be four-fifths of the way to a Golden Slam -- victories in all four Grand Slam tournaments and Olympic gold in the same calendar year.

The Serb already won the Australian and French Opens as well as Wimbledon this year. Now he needs the Tokyo title and the US Open trophy to complete the unique collection.

Steffi Graf was the only tennis player to achieve the Golden Slam in 1988.

"I'm obviously very pumped and inspired to make history," Djokovic said. "I have that guiding star that is there and I see it and it gives me light and it gives me energy, but at the same time I better stick to the stuff that I know works well on a daily basis for me."

Djokovic's next opponent will be 16th-seeded Alejandro Davidovich Fokina of Spain, who defeated John Millman of Australia 6-4, 6-7 (4), 6-3.

This is Osaka's first event since she withdrew from the French Open in May, revealing that she has dealt with depression. She then sat out Wimbledon.

Two more wins and Osaka will be in line for more honors in her Olympic debut -- a medal.

"Definitely it would mean a lot for me but I know it's a process," Osaka said. "The flag is next to my name no matter what tournament I play, but I feel like the scale of this is much bigger. It's something I've been waiting for for eight years [since she turned pro in 2013]."

The second-ranked Osaka will next face 2019 French Open runner-up Marketa Vondrousova of the Czech Republic, who beat Mihaela Buzarnescu of Romania 6-1, 6-2.

In windier, cooler and more overcast conditions than the sweltering opening two days of the competition, Osaka compiled 29 winners to Golubic's 14 and had only 11 unforced errors to her opponent's 21.

Perhaps more telling was that Osaka required only 65 minutes to dispatch a player coming off a quarterfinal appearance at Wimbledon.

A few other top women struggled.

Donna Vekic of Croatia beat third-seeded Aryna Sabalenka of Belarus 6-4, 3-6, 7-6 (3), and Alison Van Uytvanck of Belgium rallied past 2016 bronze medalist Petra Kvitova of the Czech Republic 5-7, 6-3, 6-0.

Also, Paula Badosa eliminated sixth-seeded Iga Swiatek of Poland 6-3, 7-6 (4) to improve the record of Spanish women at the Games to nine wins in nine matches in singles and doubles.

In men's action, second-seeded Daniil Medvedev of ROC and fourth-seeded Alexander Zverev of Germany each advanced quickly. Medvedev beat Sumit Nagal of India 6-2, 6-1, and Zverev eliminated Daniel Elahi Galan of Colombia 6-2, 6-2.

Meanwhile, the International Tennis Federation announced that Dutch player Jean-Julien Rojer tested positive for COVID-19 and was withdrawn from the doubles tournament with partner Wesley Koolhof.

The eighth-seeded pair were scheduled to play Marcus Daniell and Michael Venus of New Zealand. Daniell and Venus received a walkover into the quarterfinals and Rojer was placed in isolation.