On his first official meeting with Zarif in a year, Assad expressed condolences to Iran, the regional epicenter of the coronavirus pandemic with 5,209 deaths from COVID-19, AFP wrote.
Iran has recorded 83,505 infections, while Syria has declared 39 cases, including three deaths.
Assad criticized the United States for keeping economic sanctions in place on countries like Syria and Iran "despite these exceptional humanitarian conditions", the Syrian presidency said in a statement.
A photo released by the presidency showed the visiting foreign minister and Syrian president sitting opposite each other, both in face masks. Zarif also wore light blue plastic gloves.
Assad condemned "ongoing encroachments by Turkey on the sovereignty and territory of Syria," in the country's north where Ankara has deployed troops, set up military posts and backed militants battling the government.
Zarif said that "the US real agenda in not lifting its cruel sanctions on countries fighting this disease has now become clear", a statement from Tehran said.
Earlier on Monday, Zarif met with his Syrian counterpart Walid al-Muallem, the Foreign Ministry in Damascus said.
They stressed "the importance of continued coordination and the exchange of information and expertise between... the two countries to enhance their ability to confront" the pandemic and "secure the necessary needs and requirements for prevention, diagnosis and treatment".
Iran, along with Russia, is one of the Syrian government's main supporters in a nine-year anti-terrorism war that has killed more than 380,000 people and forced more than half of the country's pre-war population from their homes.
Zarif last met with Assad during a visit to Damascus in April last year.