"The divestment of any such stock would send a strong signal to the Sudanese regime and those who support it about the unacceptability of the government's actions in Darfur," the group said in the letters.
More than 2 million people have been driven from their homes and thousands have been killed each month in fighting in Sudan's western Darfur region.
A U.N.-appointed commission concluded earlier this year that the Sudanese government and allied militia had systematically abused civilians in Darfur and committed war crimes as well as crimes against humanity there.
Harvard University announced last month that it was selling its stake in PetroChina <0857.HK>, a unit of state-owned oil company China National Petroleum Corp., in protest at the Khartoum government's policies in Darfur.
Harvard President Lawrence Summers said at the time that PetroChina's parent company played a leading role in Sudan's oil industry.
The International Crisis Group letter, signed by its special adviser John Prendergast and Harvard University lecturer and author Samantha Power, cited Harvard's action and said Sudan's oil sector was a particularly lucrative business whose revenues helped purchase weapons used against the people of Darfur.