Roger Federer hailed his "greatest rival" after Rafael Nadal equalled his record of 20 Grand Slam men's singles titles in devastating fashion.

"I have always had the utmost respect for my friend Rafa as a person and as a champion," the Swiss great tweeted.

In response, Nadal thanked Federer and said their relationship "means a lot".

The Spaniard continued: "As everybody know we have a very, very good relationship and we respect each other a lot and at the same time I think he is happy when I am winning and I'm happy when he is doing things well.

"In some ways it means a lot, the positive relationship we have together because we have been going through a great rivalry for a very, very long time."

Federer, who missed Roland Garros this year after knee surgery, added: "I hope 20 is just another step on the continuing journey for both of us.

"As my greatest rival over many years, I believe we have pushed each other to become better players.

"Therefore, it is a true honour for me to congratulate him on his 20th Grand Slam victory. It is especially amazing that he has now won Roland Garros an incredible 13 times, which is one of the greatest achievements in sport.

"I also congratulate his team because nobody can do this alone," Federer, 39, added. "Well done Rafa. You deserve it."

'You can't be unhappy because your neighbour has a bigger house'

Nadal was asked on court and in his post-match news conference about drawing level with Federer, but refused to acknowledge the significance of reaching 20 Grand Slam titles.

The 34-year-old said he would love to finish his career with more majors than anyone else but added - as he has on many previous occasions - that he did not want to compare himself with others.

"I have to do it my way," he said. "I'm not going to be thinking all the time, 'Novak has this one, Roger is winning the other one'.

"You can't be always unhappy because your neighbour has a bigger house than you or a bigger boat or a better phone."

Players praise 'astonishing' Nadal

Federer was not the only tennis star to praise Nadal on social media. Eighteen-time Grand Slam singles champion Martina Navratilova called the Spaniard's achievements "astonishing".

"And you are not done," she added. "Well done champion of champions!"

Australian great Rod Laver added his congratulations, calling Nadal "an inspiration".

Women's singles champion Iga Swiatek tweeted her praise for Nadal, but as a first-time winner aged 19 the Pole was reluctant to compare herself to her fellow victor.

Compatriot and two-time Grand Slam champion Garbine Muguruza called Nadal a "legend", while 2018 Roland Garros winner Simona Halep told him: "You're an example to everyone in our sport and the best we've seen. Most importantly, a great person."

Away from tennis, Indian cricket legend Sachin Tendulkar offered Nadal his congratulations too.