Gene Sykes, the chairman of the US Olympic and Paralympic Committee (USOPC), said WADA and the US Anti-Doping Agency (USADA) had been "playing ping pong with media bullets" since revelations about a 2021 doping scandal in China emerged.
USADA has been a vocal critic of WADA over the past decade.
Tensions spiked this year after reports in April said 23 Chinese swimmers had tested positive for a banned substance ahead of the 2021 Tokyo Olympics, but were cleared to compete at the Games.
US anti-doping chief Travis Tygart has consistently accused WADA of covering up the cases, which China blamed on unintentional food contamination.
Eleven of the 23 Chinese swimmers are in Paris.
The acrimony between WADA and USADA erupted into public view again on Wednesday, with the International Olympic Committee (IOC) warning US officials they could be stripped of the 2034 Winter Olympics if WADA was not respected as the "supreme authority" of the anti-doping movement.
"What we want to do is to cool the tempers and find a way for these organisations to constructively work better together," Sykes told a press conference in Paris on Thursday.
Sykes said the dispute between the two agencies had arisen due to WADA feeling "threatened" by criticism by USADA and the body's outspoken chief Tygart.
"As soon as one side comes out with a statement, the other side comes out with a statement," Sykes said. "They have not been shy about throwing rocks at each other."
WADA president Witold Banka, who has made strongly worded criticisms of USADA and Tygart, rejected the suggestion that he had been too "dramatic" in his responses.
"Everything that I said about the US anti-doping system and the role of USADA I did in a very calm way," he said in a separate press conference.
"Our expectations to our stakeholders are to follow the rules. Our role is to make sure that our stakeholders are following our regulations, rules and have national legislation in accordance with our world anti-doping code."
Banka was asked whether he would be willing to sit down with Tygart and discuss their differences.
"We are always very open for collaboration, and it's obvious that they are one of our stakeholders," he said.
"But of course, in the current situation, after all these defamatory comments, allegations, really I have to say, statements which are totally against of the principle of collaboration, it's a very difficult situation and the relations are tough," he added.
Sykes said he was optimistic that the two bodies would settle their differences.
"We believe there will be a solution to this dispute... (WADA and USADA) don't agree yet but they really haven't been talking to each other," he said.
"We're not trying to escape from the world anti-doping code. We're trying to support it and make it stronger. And actually, I think that Travis Tygart and USADA would agree with that statement.
"And what we want to do is to if you will cool the tempers and find a way for these organisations to constructively work better together."
Olympic chiefs on Wednesday awarded the 2034 Winter Games to Salt Lake City but warned the decision could be reversed if US authorities did not get in line.
Sykes said that situation would not arise.
"(It is an) amendment that allows the IOC to have an escape clause if the United States somehow undermines the world anti-doping code. We're not going to do that," he said. "We're going to try to make it stronger."
Banka rejected the idea that the amendment was designed to silence critics of WADA.
"It was not to cut criticism because we are always open for constructive criticism but it was to make sure that harmonisation of the anti-doping system is protected," he said.
