The Ice Palace, an Olympic-size skating rink in Madrid — a site of joy only months ago — is now being filled with the bodies of the dead.

The conversion of the sporting facility into a morgue underscored the dire situation in Spain, where the death toll passed 3,400 on Wednesday, ahead of China and second only to Italy in the grim tally of fatalities.

“This is a very hard week because we are in the first stages of overcoming the virus, a phase in which we are approaching the peak of the epidemic,” Salvador Illa, the Spanish health minister, told the nation.

As the crisis in Spain deepened, the country’s military made an urgent appeal to Nato for assistance.

Like many other countries, Spain has been struggling with a lack of medical supplies for testing, treatment and the protection of front-line workers.

In a statement, Nato said Spain’s military had asked for “international assistance,” seeking medical supplies to help curb the spread of the virus both in the military and in the civilian population.

The request specified 450,000 respirators, 500,000 rapid testing kits, 500 ventilators and 1.5 million surgical masks. But it was not clear when or if help would arrive.

Funeral parlors in Madrid are now handling about seven times more bodies than a week earlier, according to officials. And workers said they had not been given any of the protective gear promised by the government, Juan José López Vivas, the deputy president of the national association of funeral parlours, told the television channel La Sexta.

The conversion of the ice rink to a morgue resonated across the country.

“This surface, which has given me so many good hours, as well as some difficult moments, can now help people who have lost their loved ones take them to wherever they wish,” Spain’s two-time world champion figure skater, Javier Fernández, said.