All four were on a “deconfliction” list of medical facilities provided by the United Nations to all sides, including Russia, in an effort to reduce civilian casualties.
The Russian foreign ministry has not commented on the report.
Russian and Syrian government forces launched an offensive against the Idlib pocket on April 30.
Human rights groups said in May that eight hospitals on the list had been targeted during the offensive.
The laws of war prohibit direct attacks on civilian facilities, like schools.
They also prohibit direct attacks against hospitals and medical staff.
However, proving culpability and intention on a battlefield is usually difficult.
International humanitarian law also grants that a school or hospital could become a legitimate target if it is used to contribute to one side’s military operations.
The Russian air force deliberately bombed at least four hospitals in rebel-controlled parts of Syria, intercepted radio messages suggest.
Russia has been accused of deliberately targeting medical facilities and personnel repeatedly since it entered the war in Syria on the side of Bashar Assad in 2015.
It has consistently denied the allegations, saying its aircraft only bomb carefully selected targets.
But in recordings of transmissions obtained by the New York Times, Russian ground controllers are heard giving pilots the precise coordinates of hospitals just minutes before they were destroyed in airstrikes.
The conversations, carried on in terse Russian military phrases, reportedly consist of a dispatcher issuing a pilot with coordinates; the pilot confirming receipt; the dispatcher giving a green light for the strike; and the pilot confirming he has hit the target.
The paper says checking the map-references use by the pilots and cross referencing the time of the transmissions with data gathered by plane spotters and witness accounts shows the aircraft were responsible for attacks on four hospitals in southern Idlib province, the last significant pocket held by rebel groups.
The Nabad al Hayat Surgical Hospital, Kafr Nabl Surgical Hospital, the Kafr Zita Cave Hospital, the Al Amal Orthopedic Hospital were all bombed in a 12 hour period on May 5 and May 6 this year.