A letter signed by 29 physicians warns that if attacks on medical facilities continue at their present rate, there could be none left within a month.
It calls on Mr Obama to impose a no-fly zone over Aleppo to stop air strikes.
Russia has meanwhile said its forces will hold fire for three hours each day from Thursday to let aid into Aleppo.
All military action, air and artillery strikes would be halted between 10:00 (07:00 GMT) and 13:00 (10:00 GMT), a defence ministry official told a briefing in Moscow.
