World number three Carlos Alcaraz edged closer to an Olympic Games showdown against Novak Djokovic on Thursday with a storming display which brought the queen of Spain to her feet.

Alcaraz, playing on the same Court Philippe Chatrier at Roland Garros where he captured the French Open in June, saw off 13th-ranked Tommy Paul of the United States 6-3, 7-6 (9/7).

The 21-year-old Alcaraz recovered from a break down in the second set to defeat Paul, having also beaten the American in the quarter-finals at Wimbledon on his way to the title at the All England Club last month.

In the second set tie-break, when he had to save a set point, the tension was too much even for Queen Letizia, who cut a nervous figure courtside before joining in a rousing standing ovation for her crowd-pleasing compatriot.

"It's all about the fight," said Alcaraz, who was playing the day after he and Rafael Nadal suffered a heartbreaking doubles loss in what was probably the veteran's final appearance at Roland Garros.

"Maybe I was a little tired from all the emotion of yesterday, playing with Rafa but I gave it everything on court," said Alcaraz.

"I had to play with intensity because Tommy is such a great athlete. I was a bit tired at the end but I just remember that I am playing for my country as well as myself."

The Spanish star will face either Casper Ruud or Felix Auger-Aliassime for a place in the gold medal match.

Top seed Djokovic, in the other half of the draw, tackles Stefanos Tsitsipas in his quarter-final later Thursday.