He estimated that as many as 117,000 people have been detained in Syrian prisons since the beginning of the uprising against the President in 2011.
As many as 70 prisoners are being kept in cells designed for no more than five people.
The information, he said, came from credible human rights groups, nongovernmental sources, as well as "intelligence assessments".
In a recent report, Amnesty International called the prison a "human slaughterhouse", claiming that every week and often twice a week between 2011 and 2015, groups of up to 50 people were taken out of their prison cells and executed.
In five years, as many as 13,000 people, most of them civilians believed to be opposed to the government, were hanged in secret and without trial.
In 2014, tens of thousands of images of dead prisoners taken by a military defector codenamed Caesar, were published to international outcry.
The victims bore the signs of starvation and torture, including gouged-out eyes, cigarettes burns and broken limbs.
Jones, in a special State Department briefing, called on Russia to take action. Moscow, Jones said, "has either aided in or passively looked away as the regime has" engaged in years of "mass murders" and other atrocities, including extensive bombing of hospitals and the use of chemical weapons on both civilians and rebel forces.
In a meeting last week in Washington, Rex Tillerson, the US Secretary of State, told his Russian counterpart, Sergei Lavrov, that "Russia must now, with great urgency, exercise its great influence over the Syrian regime".
Today's briefing is likely to have been timed in such a way as to put pressure on Russia at the start of the new round of United Nations-sponsored peace talks in Geneva.
Efforts to end the war are now proceeding along two rival tracks: the formal political process hosted at UN headquarters in Switzerland and, since January, parallel talks in the Kazakhstan capital Astana brokered by Russia, Iran and Turkey.
The US has been sidelined from talks in Astana, where most of the significant agreements of the six-year-war have been made.
Jones said the US has "reason to be sceptical" about a deal to set up "de-escalation zones" brokered by Russia during ceasefire discussions in Astana last week.