The U.S. National Hurricane Center in Miami said the storm could become a hurricane before reaching the Florida Keys and it declared hurricane and storm surge warnings for the Keys from Ocean Reef to the Dry Tortugas, including Florida Bay, with the storm expected to reach that area by Monday night or early Tuesday.
The storm had maximum sustained winds of 65 mph (100 kph) Sunday morning and it was centered over Cuba about 235 miles (380 kilometers) south-southeast of Miami. It was moving toward the north at 14 mph (22 kph).
Eta hit Cuba even as searchers in Guatemala were still digging for people believed buried by a massive, rain-fueled landslide. Authorities said at least 15 were dead and 109 were missing in Guatemala, many of them in the landslide in San Cristobal Verapaz.
Pope Francis on Sunday spoke about the population of Central America, hit "by a violent hurricane, which has caused many victims and huge damage, worsened as well by the already difficult situation due to the pandemic." Speaking to faithful gathered in St. Peter's Square, Francis prayed that "the Lord welcome the deceased, comfort their families and sustain all those so tried, as well as all those who are doing their best to help them."
In Florida, Gov. Ron DeSantis declared a state of emergency Saturday for eight counties at the end of the state as Eta approached, urging residents to stock up on supplies. South Florida started emptying ports and a small number of shelters opened in Miami and the Florida Keys for residents in mobile homes and low lying areas.
Miami-Dade County declared a state of emergency Friday night and also warned a flood watch would be in effect through Tuesday night.
Further south in the Keys, officials were monitoring the storm closely, but had no plans yet to evacuate tourists or residents. They urged residents to secure their boats and encouraged visitors to consider altering plans until Eta had passed.
Eta initially hit Nicaragua as a Category 4 hurricane, and authorities from Panama to Mexico were still surveying the damages following days of torrential rains during the week.
In Guatemala, search teams first had to overcome multiple landslides and deep mud just to reach the site where officials have estimated some 150 homes were devastated.
In the worst-hit village, Quejá, at least five bodies have been pulled from the mud. The Indigenous community of about 1,200 residents consisted of simple homes of wood and tin roofs clinging to the mountainside.
Rescue workers used a helicopter to evacuate survivor Emilio Caal, who said he lost as many as 40 family members and relatives. Caal, 65, suffered a dislocated shoulder when the landslide sent rocks, trees and earth hurtling onto the home where he was about to sit down to lunch with his wife and grandchildren. Caal said he was blown several yards (meters) by the force of the slide, and that none of the others were able to get out.
"My wife is dead, my grandchildren are dead," said Caal from a nearby hospital.
In neighboring Honduras, 68-year-old María Elena Mejía Guadron died when the brown waters of the Chamelecon river poured into San Pedro Sula's Planeta neighborhood before dawn Thursday.
Mirian Esperanza Nájera Mejía had fled her home in the dark with her two children and Mejía, her mother. But while she held tight to her children, the current swept away Mejía.
Nájera searched desperately for her mother Friday morning. But Mejía's body was later recovered.
"When the flooding started, the whole family was leaving the house," said family friend Nery Solis. "Mirian had her two children and suddenly the current grabbed them and she wasn't able to get her mom."
In southern Mexico, across the border from Guatemala, 20 people died as heavy rains attributed to Eta caused mudslides and swelled streams and rivers, according to Chiapas state civil defense official Elías Morales Rodríguez.
The worst incident in Mexico occurred in the mountain township of Chenalho, where 10 people were swept away by a rain-swollen stream; their bodies were later found downstream.
Flooding in the neighboring state of Tabasco was so bad that President Andrés Manuel López Obrador cut short a trip to western Mexico and was flying to Tabasco, his home state, to oversee relief efforts.
Hurricane Eta's arrival in northeast Nicaragua Tuesday followed days of drenching rain as it crawled toward shore. Its slow, meandering path north through Honduras pushed rivers over their banks.