Competing for the Russian Olympic Committee (ROC) team, world No. 2 Medvedev appeared to be struggling during his third round men's singles match against Fabio Fognini of Italy.
Chair umpire Carlos Ramos asked Medvedev if he could continue playing, and the player responded: "I'm a fighter, I will finish the match, but I can die," he said. "If I die, is the ITF (International Tennis Federation) going to take (sic) responsible?"
CNN has contacted the ITF for comment.
Later Wednesday, Spain's Paula Badosa left the court in a wheelchair after being forced to retire from her women's singles quarter-final match against the Czech Marketa Vondrousova due to heatstroke.
Badosa lost the first set 6-3 before requiring a medical timeout ahead of the start of the second set.
After lengthy treatment, Badosa was unable to continue and retired from the match.
"I have suffered a heat stroke as you all have seen, and I did not feel fit to continue competing in the match," Badosa said in comments posted by Tokyo 2020.
"It was a shame to end my participation this way. The conditions have been demanding from day one, we tried to adapt as best as possible, but today the body has not resisted as needed."
After the match, Vondrousova revealed she is taking special measures to deal with the conditions.
"In the match, I use the ice towels and also use the air tube... it's very nice," she said. "I also have some gels."
Tokyo temperatures reached the upper 80s Fahrenheit on Wednesday.
"The risk for heat exhaustion and heat stroke remains," according to CNN's weather team, which added that the high humidity "makes it very difficult for the body to cool itself naturally."
25-year-old Medvedev also addressed the conditions after the match, which he won 1-6 6-1 6-3.
"Even from the first set, I didn't feel good enough with my breathing. That's why I called the physio. I felt like my diaphragm had blocked. I couldn't breathe properly. I think it was the most humid day we have had so far," he said in comments posted by Tokyo 2020.
"Then, on the second set, I just had darkness in my eyes, like between every point I didn't know what to do to feel better. I was bending over, and I couldn't get my breathing together. I was ready to just fall down on the court."
Fognini agreed that the conditions were "really tough" in a post-match interview. "It's hard to play at 11 a.m. with this humidity," he said.
Medvedev said he had taken a freezing cold shower during a break following the first set, which made him feel better.
Asked whether he thought the roof of the arena should be closed to improve conditions, Medvedev said that might make things worse, instead suggesting matches should start later in the day.
"I said it in the first round, and I'll continue saying it," said Medvedev, who is known as one of the most outspoken and controversial players in men's tennis.
On Saturday, world No. 1 Novak Djokovic described conditions as "brutal" following his first-round win and said he agreed with Medvedev's call at the weekend to move matches to later in the day.
Nonetheless, other players have said they aren't feeling any adverse effects from the conditions.
"We're Aussies, we're alright," said Australia's Ashleigh Barty.
Late Wednesday, the ITF did announce schedule changes, with matches to begin at 3 p.m. local time from Thursday.
The decision was made "in the interests of player health and welfare" and following "extensive consultation" with players, referees, medical experts and other key stakeholders, among others, the ITF said in a statement.
The ITF reiterated that players could request 10-minute breaks during play should temperatures exceed 30.1°C (86 Fahrenheit).
Mark Adams, spokesperson for the International Olympic Committee (IOC), said a "whole range of measures are being taken" to deal with the heat.
Adams cited the decision to move the marathon and race walk to the city of Sapporo, 400 miles north of Tokyo, and moving events such as the 5,000 meter athletics to later in the day.
Adams said tennis judges have been wearing "cooling underbody armor that cools them down" and there are a lot of "ingenious solutions" that are allowing events to go ahead.
"I think so far it's been a few small minor issues, but so far things seem to be going very well indeed," Adams said.
When Tokyo last hosted the Olympics in 1964, it did so in the cooler month of October. But broadcasting demands now stipulate that the Games are held in July or August, according to Reuters -- a more favorable slot for TV networks.