Storm Otto smashed into southeastern Nicaragua on Thursday as a category 2 hurricane before crossing into Costa Rica but weakened rapidly and became a tropical storm by early Friday.
Tropical storm Otto killed at least nine people and caused extensive damage in Costa Rica before moving out into the Pacific Ocean, officials said on Friday.
Costa Rican President Luis Guillermo Solis decreed three days of mourning to begin on Monday.
Aerial television pictures from northern Costa Rica showed water and mud in several towns, and small bridges collapsed.
Solis said the storm dumped a month's worth of rain in just a few hours in Costa Rica. Authorities said it caused around $8 million in damage to roads.
Otto smashed into southeastern Nicaragua on Thursday as a category 2 hurricane before crossing into Costa Rice, but it weakened rapidly and became a tropical storm by early Friday as it drifted deeper into the Pacific, the US National Hurricane Center said.
A Costa Rican police official, Walter Espinoza, told a news conference: "The number of people killed is nine. We have recovered eight bodies, only one remains."
Updating an earlier death toll of four, Espinoza said five of the nine people killed died in Upala, a town near the border with Nicaragua that found itself in the storm's path.
In Nicaragua, the government's spokesperson, First Lady Rosario Murillo, said: "Up to now, thank God, we haven't counted any loss of human life."
Officials in both countries had evacuated the most at-risk areas before the hurricane hit, and closed schools and mobilised emergency crews.
Officials in Costa Rica said 5,500 people had been put up in shelters.
Nicaragua had 44 shelters operating for many of the 10,500 people who had been evacuated.
UN agencies and non-governmental organisations had supported the emergency response, the UN office coordinating humanitarian affairs said in a statement.