Daniil Medvedev looked like he had a point to prove as he got preparations for his US Open title defence back on track with a 6-4 7-5 win over Botic van de Zandschulp in the second round of the Cincinnati Open.

Medvedev had been building momentum ahead of the year's last Grand Slam at Flushing Meadows by winning a tune-up event in Los Cabos without dropping a set but was beaten by Nick Kyrgios in the second round of the Canadian Masters in Montreal last week.

Playing against the only man to take a set off him in his 2021 US Open title run, the Russian starting strongly against Dutchman Van de Zandschulp on Tuesday with an immediate break before going on to win the first set.

The second set posed more of a challenge, with the world No.1 one having to save a set point, but he capitalised on several double-faults from Van de Zandschulp before wrapping up the match.

Medvedev will face either American Tommy Paul or Canada's Denis Shapovalov in the next round,with a potential rematch with Kyrgios looming in the quarter-finals of this last tune-up event before the US Open, which begins on August 29 in New York.

Kyrgios quickly regained his composure after losing his temper during a 7-5 6-4 win over Alejandro Davidovich Fokina to reach the second round, where he will face in-form American Taylor Fritz.

Kyrgios appeared in complete control when he fired down an unreturnable serve to capture the first set and went up a break early in the second.

But when the Spaniard levelled at 2-2 it prompted the fiery Australian to launch a ball into the stands in a moment reminiscent of his win over Stefanos Tsitsipas at Wimbledon, where the Greek did the same thing and Kyrgios argued unsuccessfully that he should be defaulted for it.

But Kyrgios quickly regained his cool, holding to love in the next game and sealing the victory with another massive serve.

Fritz's powerful serving and aggressive returns resulted in a 6-1 6-1 victory over Argentine Sebastian Baez earlier in the day. The win was the 11th seed's 33rd of the year.

Italy's Jannik Sinner, seeded 10th, emerged with a 6-7 (11-9) 6-4 7-6 (8-6) victory over Australia's Thanasi Kokkinakis to improve to 37-10 on the year.

In other first-round action at the Masters 1000 tournament, American Paul beat compatriot Jenson Brooksby 6-3 6-2, Australia's Alex de Minaur dispatched Swiss Henri Laaksonen 6-2 6-2, Croatian Borna Coric defeated Lorenzo Musetti 7-6(2) 6-3 and Spaniard Albert Ramos-Vinolas beat Italy's Fabio Fognini 6-2 6-3.

In other second round matches, third seed Carlos Alcaraz beat American wildcard Mackenzie McDonald 6-3 6-2, 14th seeded Marin Cilic downed Emil Ruusuvuori 6-4 6-7 (7-5) 7-5 and 13th seed Diego Schwartzman downed Aslan Karatsev 7-6 (7-3) 3-6 6-2.