Khashoggi, a USA resident who wrote for The Washington Post and had been critical of Prince Mohammed, was lured to the Saudi consulate in Istanbul to get marriage documents on October 2, where he was killed and reportedly dismembered.
British PM Theresa May told the prince that the killers of Khashoggi should be held to account, her office said after the two leaders met.
The crown prince patted Mr Putin's hand three times for emphasis as the two leaders took their seats next to each other.
Mrs May's appointment with... She joined the leaders of other industrialized nations such as China, Russia, and the USA, at an annual summit on world trade that also draws counterprotesters.
Britain exported more than £6 billion in goods and services to Saudi Arabia in 2017 including machinery, cars and aircraft.
"She encouraged Crown Prince to ensure Saudi Arabia co-operated fully with Turkish authorities and worked to bring both investigations to an acceptable close". World leaders who meet with the Crown Prince should raise these serious allegations.
2018 in Buenos Aires. Ludovic Marin AFP Getty images
"They exchanged pleasantries at the leaders' session as he did with almost every leader in attendance", the White House official said on Friday.
He was welcomed by Argentina's President Mauricio Macri at Costa Salguero in the capital at the start of the G20 Leaders' Summit.
Despite initial pleasantries, the crown prince looked sidelined during the official "family photo" of world leaders and other dignitaries, standing at the far edge of the group portrait and ignored.
US President Donald Trump, who has touted the country's lucrative purchase of arms from the US, has threatened to veto the bill if it arrives on his desk.
Police, coast guard and border patrol officers roped off a 12-square-kilometer (5-square-mile) area near the Buenos Aires convention center, where the summit is taking place.