Oil prices will fall further before Saudi Arabia and Russia agree to call off their price war, KKR Global Institute managing director Neil Brown said Tuesday.

On a Council on Foreign Relations conference call, Brown predicted oil would continue to fall over "weeks and months" before the two sides sit back down and agree to bury the hachet.

"President [Vladimir] Putin and Mohammed bin Salman will have to be the ones to make the call on when to change policy," said Brown.