Khashoggi, a Washington Post columnist, disappeared inside the Saudi consulate in Istanbul.
During the five-minute exchange, Salman is heard urging Macron not to worry, to which the French president promptly replied, "I am anxious".
Mr Macron says: "You never listen to me", to which the Crown Prince replies: "I will listen, of course".
In an image that quickly went viral online, Russian President Putin and the 33-year-old prince grinned broadly and gave each other an effusive handshake as if they were long-lost friends reunited at the G-20.
The conversation between Macron and MBS took place in Buenos Aires as world leaders arrived in the Argentinian capital for the G20 summit.
Mattis said the meeting included exhaustive discussions and that lawmakers expressed frustration with U.S. support to Saudi Arabia.
Theresa May used a meeting with the Saudi Crown Prince at the G20 summit to "encourage" him to make sure Saudi Arabia co-operates in the investigation into murdered journalist Jamal Khashoggi.
Furthermore, the English-language Saudi Gazette shared a video of the meeting reportedly showing a cryptic exchange between the pair on the killing of Khashoggi.
Video surfaces of Chiefs RB Kareem Hunt's alleged February altercation with woman
The video shows Hunt arguing with a woman, Abigail Ottinger , a 19-year-old Kent State student, in the hotel's hallway. In addition, calls to Hunt's agent, Dan Saffron, and the Cleveland Police Department were not immediately returned.
The BBC's political editor Laura Kuenssberg wrote on Twitter that 'The Prime Minister stressed the importance of ensuring that those responsible for the appalling murder of Jamal Khashoggi are held to account'.
It says Mr Macron told MBS that Europeans wanted global investigators to take part in the probe on Mr Khashoggi's death and stressed "the necessity of a political solution in Yemen".
At the end, Mr Macron is heard threateningly telling MBS: "I am a man of my word".
Instead the USA president appeared to barely acknowledge MBS, as he's known, before taking his place for the photo between French President Emmanuel Macron and Japanese Prime Minister Shinzo Abe.
Proposed US congressional legislation on Yemen, even if passed, is unlikely to impact on Saudi Arabia's ability to pursue the war in Yemen due to available Egyptian, Emerati, and Israeli support. Saudi Arabia claims that the prince had no prior knowledge of the murder.
G20 powers opened two days of summit talks, after a stormy buildup dominated by tensions with Russian Federation and US President Donald Trump's combative stance on trade and climate fears.
He is facing pressure from some leaders including the UK, France, Germany and Turkey's President Erdogan, who is also in attendance in Argentina, to admit exactly what happened.
A White House official confirmed the two exchanged pleasantries during a leaders' session.