In the video, the Saudi prince can be heard telling the French president "Don't worry", to which he replies, "I am anxious".
The Elysee said it was the first time that Macron and the crown prince, known as MbS, had spoken since Khashoggi's murder at the Saudi consulate in Istanbul on Oct 2.
Mr Putin's spokesman Dmitry Peskov reportedly greeted news of the cancellation by saying that while it was regrettable, it left the Russian president with a couple of extra hours to meet other leaders on the sidelines of the summit.
Prince Mohammed's presence at the worldwide summit has been contentious following the killing of Saudi journalist Jamal Khashoggi at a Saudi consulate in Istanbul in October.
Saudi Arabia's public prosecutor has said the Crown Prince knew nothing of the operation to kill Khashoggi. But it received wide traction on social media, with Macron telling the prince, "You never listen to me", to which Prince Mohammed replies, "I will listen, of course".
Mrs May is said to have told the Crown Prince to take action to prevent future incidents like the murder of Mr Khashoggi from happening.
French President Emmanuel Macron stepped up pressure on Salman over Khashoggi's killing by telling him global experts need to be involved in the murder investigation.
At the end Macron can be heard saying: "I am a man of my word".
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'She encouraged Crown Prince to ensure Saudi Arabia co-operated fully with Turkish authorities and worked to bring both investigations to an acceptable close.
A White House official confirmed the two exchanged pleasantries during a leaders' session.
Mattis and Pompeo urged senators to support the United States involvement in the war in Yemen, including assistance to Saudi Arabia.
In a five-minute exchange on the sidelines of the G20 summit in Argentina, Macron conveyed "very firm" messages to the prince over the killing and the need to find a political solution for the situation in Yemen, an Elysee official also said.
During the course of the day, President Trump "exchanged pleasantries" with Salman, telling reporters that while they didn't talk about hot-button issues concerning the USA and Saudi Arabia, it was possible the pair would do so as the summit rolled on.
The demonstrators also accused the G20 group of countries of concentrating too much on financial interests and globalization, while condemning austerity measures proposed by Argentina's government and backed by the International Monetary Fund, a dignitary at the summit.
"We might [later], but we had none", President Trump told the press pool.