MANAGUA, Nicaragua (AP) _ The Roman Catholic Church and opposition political, labor and business leaders set up a private relief group Wednesday to solicit international aid for Nicaraguans left homeless by Hurricane Joan.

Cardinal Miguel Obando y Bravo, archbishop of Managua, was elected coordinator of the Complementary Commission, so named because it is designed to complement government relief efforts.

About 200,000 Nicaraguans lost their homes when the hurrican swept across Nicaragua Oct. 22, downing bridges and destroying crops with torrential rains and winds. The Atlantic coast and the south-central regions were hardest hit.

President Daniel Ortega said Friday the storm killed 116 people and left 110 missing.

The leftist Sandinista government urgently appealed to the international community for aid. Reynaldo Antonio Tefel, president of the government's National Emergency Committee, said Tuesday the amount of aid received so far - 2,236 tons of supplies - would cover the needs of the homeless for about a month.

Other representatives to the newly formed relief group include: Mauricio Diaz, a leader of the Popular Social Christian Party; Virgilio Godoy of the Liberal Independent Party; Gilberto Cuadra of the Superior Private Enterprise Council; Gustavo Tablada of the Nicaraguan Socialist Party; and Pablo Antonio Cuadra, director of the opposition newspaper La Prensa.

The group said in a statement it was ''provisional'' and that other non- governmental organizations could participate.

On Wednesday, the international relief organization World Vision flew about $67,000 worth of supplies from Newark, N.J. to hurricane victims here in what organizers said was the first such effort from the East Coast.

The supplies included 14,000 blankets, said Mike Schwager, a group spokesman. He said World Vision sent other supplies, including water-purifying tablets and tents, in an airlift from Los Angeles last week.