PONCE, Puerto Rico (AP) _ Rescue workers on Saturday began a final, 72-hour search for survivors of the mudslide that buried the Mamayes shantytown five days earlier.

Gov. Rafael Hernandez Colon said the government would erect a monument to the hundreds of people believed killed in the disaster and would not allow houses to be rebuilt in the Mamayes area, on a steep ridge at the base of a mountain. The town was devastated Oct. 7 by a mudslide triggered by a tropical deluge.

''We are going to convert it into a green area where there is going to a monument with the names of those who died there,'' Hernandez Colon said after visiting the area and talking to leaders of the more than 300 people involved in the search.

Rescue workers remained hopeful of finding more survivors.

''I think there's a small chance there's someone out there alive, but it's extremely unlikely,'' said Ken Hulick, an Atlanta-based U.S. Park Service official directing the 21 American search-dog teams sniffing through tons of mud and debris at Mamayes.

After barking dogs brought them to a collapsed house Saturday, National Guardsman dug out the 36th body recovered from Mameyes, where hundreds of people are still believed missing.

Eighty people have been confirmed dead islandwide from floods and landslides caused when 10 to 15 inches of rain fell last weekend.

Hulick said that by Sunday night, the search dogs will ''have covered every inch,'' except for areas too unstable to walk on. On Monday, the U.S. Army Corps of Engineers with special listening devices will make a final sweep of the area, and then ''turn it over to the National Guard.''

National Guard Col. Gilberto Moreno said heavier equipment would be used after Monday to clear heavy debris to speed up recovery of bodies.

''Every effort will be made to protect the bodies,'' Moreno added.

Dr. Giordano San Antonio, health director for the southern region, said seven children in three refugee shelters had measles, and doctors were vaccinating all children under age 15 in the shelters.

He said some 3,000 people were in shelters in the region. Officials said more than 5,000 people were in shelters around the island.

Meanwhile, a 12-member team from Washington arrived and went to Mamayes and met with Commonwealth officials.

The team includes Sam Speck, associate dirctor of the Federal Emergency Management Agency; Maj. Gen. Henry Hatch, director of civil works for the Army Corps of Engineers; and Col. Edward Bruner of the Department of Army in the Pentago.

Hatch said the Department of Defense had flown in 4,000 cots from Richmond, Va.; 200 tents from Ogden, Utah; a water distribution system from Warner Robins, Ga.; and two Bailey bridges from Pueblo, Colo. The material was from war reserve stocks at military bases, he said.

President Reagan has declared Ponce and three other municipalities federal disaster areas, but officials said more areas might later be eligible for federal disaster relief.

Ponce Mayor Jose Dapena Thompson has estimated damage from the storm at $100 million in the southern region.

In Washinton, the Puerto Rico Federal Affairs Administration said it was collecting money to aid flood victims. It said donations could be sent to its office at 734 15th St. NW, Suite 700, Washington, D.C., 20005.