President Carter's long-promised review of federal policies in cultural matters ground slowly underway yesterday with a public meeting of the Federal Council on the Arts and the Humanities in the Indian Treaty Room of the Old Executive Building.

Joan Mondale, the honorary chairman, said she hoped the deliberations of the council would culminate in a single final report that would stress that assistance to art and humanities must flow through many channels and allow for innovation.

Chairman Joseph D. Duffey, who heads the National Endowment for the Humanities, said White House conferences on the arts and the humanities, voted by Congress are to be planned when funds are appropriated this fall. The conference said Duffey will deal with the future of our culture and the cultural activities of all government agencies.

Alfred Stern, who handles cultural matters on the White House staff, said that by next December several White House task forces would study career problems, an inventory of cultural resources, international aspects, public design and architecture, and the relation between the mdeia and culture. "Arts policy is as important as urban policy," Stern said.

The Federal Council was established by Congress in 1965 and is meant to coordinate the arts and humanities endowments and the new Institute of Museum Services. It consists of the heads of 14 interested federal agencies. Yesterday's meeting was the first in many years.

Chairman Duffey established a working group to propose operating procedures for the council which is to be enlarged to include all agencies involved in fostering the arts, including the Defense Department.

The meeting also established working groups on museum procedures and on U.S. cultural representation abroad. It heard a lengthy report by Joshua Taylor, director of the National Collections of Fine Arts, on the so-called "Arts and Artifacts Indemnity Act" of 1975, under which foreign exhibits such as the just-opened "Splendor of Dresden" show at the National Gallery are insured against loss or damage.