New York - Rafael Nadal revealed on Tuesday he had offered to provide Andy Murray with his boat in Mallorca, where the Scot is playing in a second-tier Challenger event as part of his comeback following hip surgery.

The Spaniard swept into the second round of the US Open with a 6-3, 6-2, 6-2 rout of Australian world number 60 John Millman on the same day as Murray won his second singles match at a tournament that bears Nadal's name.

"I'm very happy to have Andy Murray playing there," Nadal said. "It's great news for us, of course, but for him and for the world of sport that's great news and I wish him the very best.

"I just text him a couple days ago saying, 'If you need anything, just let me know. You want to go out with the boat or anything, I can help you, just let me know.'"

Murray, playing on the Challenger circuit for the first time in 14 years, defeated 115th-ranked Norbert Gombos of Slovakia 6-3, 6-4 in an event he is using to rebuild his singles form.

The three-time Grand Slam champion underwent a hip operation in January following his first-round exit from the Australian Open and began easing his way back by playing doubles, starting with a title at Queen's in June.

"Best of luck, and more than playing in my home it is great news that he is back on the tennis court playing singles after a lot of struggles in recent years. I am happy for him, it is very special," Nadal said.

"The decision to go and play a challenger is because he feels well, my feeling, the way that I see it.

"If you don't feel it very well, you play normal tour and just let's see how it goes. If one player like Andy is able to go and play a challenger is because physically he feels well and he wants to play matches."

Nadal has his sights fixed on a fourth US Open crown this fortnight and will face another Australian, Thanasi Kokkinakis, in the second round after taking just over two hours to see off Millman, the player who stunned Roger Federer in the last 16 here a year ago.

"I'm happy the way that I was able to win tonight. It's a good start," Nadal said.

"It's very special to be back in the night session at Arthur Ashe Stadium. The beginning, the first match, is always a little bit new even if I've played here plenty of times.

"I think I had more or less positive feelings tonight," he added. "I need to keep improving every single day. Winning with that result allows me more to have a good practice. I hope to be ready for after tomorrow knowing it's a tough challenge, Thanasi in the second round."

Results from Tuesday's second day of the US Open tennis championships: (x denotes seed):

Men

First round





Andrey Rublev (RUS) bt Stefanos Tsitsipas (GRE x8) 6-4, 6-7 (5/7), 7-6 (9/7), 7-5

Gilles Simon (FRA) bt Bjorn Fratangelo (USA) 5-7, 7-5, 7-5, 7-5

Matteo Berrettini (ITA x24) bt Richard Gasquet (FRA) 6-4, 6-3, 2-6, 6-2

Jordan Thompson (AUS) bt Joao Sousa (POR) 6-3, 6-2, 6-4

Alexei Popyrin (AUS) bt Federico Del Bonis (ARG) 6-1, 7-5, 7-6 (7/5)

Mikhail Kukushkin (KAZ) bt Roberto Bautista Agut (ESP x10) 3-6, 6-1, 6-4, 3-6, 6-3

Gael Monfils (FRA x13) bt Albert Ramos (ESP) 7-6 (7/2), 6-4, 6-3

Marius Copil (ROU) bt Ugo Humbert (FRA) 6-3, 5-7, 7-6 (13/11), 4-6, 6-1

Denis Shapovalov (CAN) bt Felix Auger-Aliassime (CAN x18) 6-1, 6-1, 6-4

Pablo Andujar (ESP) bt Kyle Edmund (GBR x30) 3-6, 7-6 (7/1), 7-5, 5-7, 6-2

Lorenzo Sonego (ITA) bt Marcel Granollers (ESP) 6-3, 6-4, 6-4

Alexander Bublik (KAZ) bt Santiago Giraldo (COL) 2-6, 6-0, 7-5, 3-6, 6-4

Thomas Fabbiano (ITA) bt Dominic Thiem (AUT x4) 6-4, 3-6, 6-3, 6-2

Alexander Zverev (GER x6) bt Radu Albot (MDA) 6-1, 6-3, 3-6, 4-6, 6-2

Frances Tiafoe (USA) bt Ivo Karlovic (CRO) 6-2, 6-3, 1-2, retired

Aljaz Bedene (SLO) bt Jozef Kovalík (SVK) 6-3, 6-4, 7-5

Benoît Paire (FRA x29) bt Brayden Schnur (CAN) 6-2, 6-4, 6-4

Diego Schwartzman (ARG x20) bt Robin Haase (NED) 6-3, 7-6 (8/6), 6-0

Egor Gerasimov (BLR) bt Lloyd Harris (RSA) 7-5, 7-6 (7/5), 7-6 (7/3)

Tennys Sandgren (USA) bt Jo-Wilfried Tsonga (FRA) 1-6, 6-7 (2/7), 6-4, 7-6 (7/5), 7-5

Vasek Pospisil (CAN) bt Karen Khachanov (RUS x9) 4-6, 7-5, 7-5, 4-6, 6-3

John Isner (USA x14) bt Guillermo Garcia-Lopez (ESP) 6-3, 6-4, 6-4

Jan-Lennard Struff (GER) bt Casper Ruud (NOR) 6-4, 6-4, 6-2

Cedrik-Marcel Stebe (GER) bt Filip Krajinovic (SRB) 6-3, 4-6, 6-4, 7-6 (8/6)

Marin Cilic (CRO x22) bt Martin Klizan (SVK) 6-3, 6-2, 7-6 (8/6)

Fernando Verdasco (ESP x32) bt Tobias Kamke (GER) 6-3, 3-6, 6-1, 6-2

Chung Hyeon (KOR) bt Ernesto Escobedo (USA) 3-6, 6-4, 6-7 (5/7), 6-4, 6-2

Thanasi Kokkinakis (AUS) bt Ilya Ivashka (BLR) 6-3, 7-6 (10/8), 6-7 (4/7), 6-2

Rafael Nadal (ESP x2) bt John Millman (AUS) 6-3, 6-2, 6-2

Antoine Hoang (FRA) bt Leonardo Mayer (ARG) 3-6, 6-2, 6-7 (6/8), 6-1, 6-3

Henri Laaksonen (SUI) bt Marco Cecchinato (ITA) 7-6 (7/3), 7-6 (8/6), 2-6, 3-6, 7-6 (7/2)

Nick Kyrgios (AUS x28) bt Steve Johnson (USA) 6-3, 7-6 (7/1), 6-4

Women

First round





Naomi Osaka (JPN x1) bt Anna Blinkova (RUS) 6-4, 6-7 (5/7), 6-2

Magda Linette (POL) bt Astra Sharma (AUS) 6-3, 6-4

Cori Gauff (USA) bt Anastasia Potapova (RUS) 3-6, 6-2, 6-4

Timea Babos (HUN) bt Carla Suarez Navarro (ESP x28) 6-2, 0-0, retired

Anett Kontaveit (EST x21) bt Sara Sorribes (ESP) 6-1, 6-1

Ajla Tomljanovic (AUS) bt Marie Bouzková (CZE) 1-6, 7-5, 6-1

Alize Cornet (FRA) bt Jessica Pegula (USA) 6-2, 6-3

Belinda Bencic (SUI x13) bt Mandy Minella (LUX) 6-3, 6-2

Kaia Kanepi (EST) bt Tatjana Maria (GER) 5-7, 7-6 (7/4), 6-3

Julia Görges (GER x26) bt Natalia Vikhlyantseva (RUS) 1-6, 6-1, 7-6 (7/1)

Francesca Di Lorenzo (USA) bt Veronika Kudermetova (RUS) 7-6 (7/4), 6-2

Anastasia Pavlyuchenkova (RUS) bt Pauline Parmentier (FRA) 6-1, 7-6 (7/2)

Kiki Bertens (NED x7) bt Paula Badosa (ESP) 6-4, 6-2

Simona Halep (ROU x4) bt Nicole Gibbs (USA) 6-3, 3-6, 6-2

Taylor Townsend (USA) bt Kateryna Kozlova (UKR) 3-6, 6-3, 6-2

Sorana Cirstea (ROU) bt Katerina Siniakova (CZE) 7-5, 6-2

Aliona Bolsova (ESP) bt Barbora Strycova (CZE x31) 6-3, 0-6, 6-1

Caroline Wozniacki (DEN x19) bt Wang Yafan (CHN) 1-6, 7-5, 6-3

Danielle Collins (USA) bt Polona Hercog (SLO) 6-3, 4-6, 6-4

Kirsten Flipkens (BEL) bt Wang Xiyu (CHN) 3-6, 6-2, 6-2

Bianca Andreescu (CAN x15) bt Katie Volynets (USA) 6-2, 6-4

Kristie Ahn (USA) bt Svetlana Kuznetsova (RUS) 7-5, 6-2

Jelena Ostapenko (LAT) bt Aleksandra Krunic (SRB) 6-3, 7-6 (9/7)

Alison Riske (USA) bt Garbine Muguruza (ESP x24) 2-6, 6-1, 6-3

Elise Mertens (BEL x25) bt Jil Teichmann (SUI) 6-2, 6-2

Kristyna Pliskova (CZE) bt Diane Parry (FRA) 6-4, 6-3

Andrea Petkovic (GER) bt Mihaela Buzarnescu (ROU) 6-3, 6-4

Petra Kvitova (CZE x6) bt Denisa Allertova (CZE) 6-2, 6-4

Donna Vekic (CRO x23) bt Richel Hogenkamp (NED) 7-6 (7/4), 6-3

Yulia Putintseva (KAZ) bt Madison Brengle (USA) 6-3, 6-3

Aryna Sabalenka (BLR x9) bt Victoria Azarenka (BLR) 3-6, 6-3, 6-4

Anna Kalinskaya (RUS) bt Sloane Stephens (USA x11) 6-3, 6-4