Velayati, a 67-year-old US-educated physician, said he would make free health treatment available if elected on June 14, in a speech at Shahid Beheshti University in Tehran.
"Some people cannot afford to go to doctors, or pay for their medicines and treatment," he said.
Iran, under harsh international sanctions over its disputed nuclear programme, is facing increasing difficulties in importing medicine as its access to the global banking system is "severely affected" by the measures, officials and local reports said.
Velayati, one of the eight presidential candidates approved by unelected electoral watchdog the Guardians Council, also seeks to "boost Iran's capacity to produce medicine and medical equipment" and revamp an "ineffective" insurance system.
The presidential election is overshadowed by economic strife, at a time when Iran is still at loggerheads with Western powers who accuse it of seeking to develop an atomic bomb. Tehran has repeatedly denied these claims.
Velayati's remarks come as many Iranian patients say they cannot afford the spiralling cost of drugs for life-threatening and complex illnesses, including cancer and multiple sclerosis.
In October, an Iranian official acknowledged the price of domestically-manufactured medicines had increased by 15 to 20 percent over the previous three months, and that of imported drugs by 20 to 80 percent.
Western economic sanctions have affected some six million patients in Iran.
Fatemeh Hashemi, head of the Foundation for Special Diseases, said the international measures have caused a hike in prices and even "shortages" in some sectors.
Iran's currency has lost more than two thirds of its value since early 2012, and its economy is struggling against rising inflation, officially estimated at more than 30 percent, and a double-digit unemployment rate.
Iran claims it is managing to produce some of its drugs requirements and is moving towards "self-sufficiency," but it criticises the sanctions for targeting imports of medication.
Iranian-made medicines are generally cheaper than imported drugs, but doctors are cautious about prescribing them and patients prefer treatment with the imported brands.