An estimated 450 dogs and 350 cats were left when the town's residents were evacuated after the initial May 2 eruption, the volcano's first in thousands of years.
"They asked us to bring food for the pets, and police and soldiers would feed the animals," said Alejandra Cassino, a representative of the animal welfare group, at a small demonstration in Santiago. The group is lobbying for access and enough time to retrieve the animals.
"There are some people among us thinking of a commando operation to reach the town," Cassino said.
Authorities have established an exclusion area of 30 miles around the volcano, forcibly evicting holdouts included farmers reluctant to abandon livestock.
The government is removing livestock by the hundreds and offering cash payments to owners for animals that do not survive.
Cassino said rescuing cats and dogs would take at least 48 hours, "because we would have to chase the pets, sedate many of them, separate them, put them in cages."
The group's international coordinator, Adriana de La Garza, said soldiers have been feeding the pets occasionally but she had no details.
President Michelle Bachelet visited the region Saturday as the volcano continued to churn out large amounts of ash and smoke, in a cloud that extends for thousands of miles east across Argentina and Uruguay.