Daniil Medvedev, of Russia, returns a shot from Andy Murray, of Britain, during the Miami Open tennis tournament, March 26, 2022, in Miami Gardens, Florida. (WILFREDO LEE / AP)

Top seed Daniil Medvedev moved a step closer to reclaiming the world No 1 ranking as he beat Spaniard Pedro Martinez 6-3 6-4 on Monday to reach the last 16 at the Miami Open while Naomi Osaka cruised into the quarter-finals of the women's draw.

Daniil Medvedev, who can replace Novak Djokovic on top of the world rankings if he reaches the Miami semi-finals, fired down 14 aces, won 79 percent of his first-serve points and broke Martinez three times to secure victory in 84 minutes

Medvedev, who can replace Novak Djokovic on top of the world rankings if he reaches the Miami semi-finals, fired down 14 aces, won 79 percent of his first-serve points and broke Martinez three times to secure victory in 84 minutes.

"I just felt like I had to be more consistent, and the more consistent one today would win," Medvedev said.

"I managed to just make a few less errors at important moments, serve even better, and it was a small margin but I managed to win and I'm really happy."

Up next for the Russian, who lost his world number one ranking after a surprise third-round loss at Indian Wells two weeks ago, will be American Jenson Brooksby, a 6-3 5-7 6-4 winner over Spanish 15th seed Roberto Bautista Agut.

Spanish 14th seed Carlos Alcaraz will meet Greek third seed Stefanos Tsitsipas in a mouth-watering fourth-round clash after both enjoyed straight-set wins over Marin Cilic andAlex de Minaur respectively.

The 18-year-old Alcaraz beat Tsitsipas in their only previous meeting, a five-set thriller in the third round of last year's US Open.

"He is a great player," Tsitsipas said of Alcaraz.

"For me it will be a great challenge, the ones that I like."

Indian Wells champion Taylor Fritz converted both of his break point opportunities to dispatch fellow American Tommy Paul 7-6(2) 6-4 and will meet Serbian Miomir Kecmanovic, a 7-6(4) 6-3 winner over Sebastian Korda.

Fritz said it is all about managing expectations.

"I didn't really think about winning Indian Wells until I had match point in the final," he said.

"So I'm approaching this one the same way. I don't expect to win the tournament, but I take it one match at a time, and you never know."

READ MORE: Medvedev sees path back to the top through Miami Open

Osaka serves up win

Naomi Osaka, of Japan, celebrates a point against Alison Riske during the Miami Open tennis tournament, March 28, 2022, in Miami Gardens, Florida. (WILFREDO LEE / AP)

Japan's Osaka reached the quarter-finals for a second consecutive year with a 6-3 6-4 win over American Alison Riske during which she won 70 percent of her first-serve points and recovered after falling behind 2-0 in the second set.

After the match the unseeded Osaka expressed how she is in a different state of mind than last year when arriving at the Miami Open ranked second after winning the Australian Open.

"It's really funny for me because last year I made it to the (Miami) quarters too but it was after I won Australia and I wasn't that grateful, I kind of expected to win," said Osaka.

ALSO READ: Osaka cruises past Kerber to reach third round in Miami

"But I'm in the same position this year and I am so like, this is really like one of the funnest times of my life."

Standing between four-times Grand Slam champion Osaka and a first Miami semi-final spot will be ninth-seeded Australian Open finalist Danielle Collins, who beat Tunisian eighth seed Ons Jabeur 6-2 6-4.

Poland's new world No 1 Iga Swiatek eased past 14th seed Coco Gauff 6-3 6-1 and will next face Petra Kvitova after the Czech defeated Veronika Kudermatova 7-6(5) 6-4 to reach the quarters.

Spanish fifth seed Paula Badosa closes out the evening session against Czech wildcard Linda Fruhvirtova.