* Downgraded to Category 3 from 4
* Passes over Florida Keys, heads towards Naples
* Streets of Miami flooded
* About 1.8 million homes, businesses without power
* First U.S. death linked to storm
FORT MYERS/MIAMI Sept 10 (Reuters) - Hurricane Irma lost some strength as it lashed southern Florida on Sunday afternoon, but forecasts warned it would remain a powerful storm as it flooded Miami streets and knocked out power to about 1.8 million homes and businesses.
All of southern Florida was feeling the storm's effects, with at least one man killed, a woman forced to deliver her own baby and trees and apartment towers swaying in high winds.
The National Hurricane Center said the storm had maximum sustained winds of 120 miles per hour (195 kph), dropping it to a Category 3, the midpoint of the five-step Saffir-Simpson scale.
Irma had been one of the most powerful hurricanes ever seen in the Atlantic, killing 28 people in the Caribbean and pummeling Cuba with 36-foot (11 meter) waves on Sunday. Its core was located about 35 miles (56 km) south of Naples by 2 p.m. ET (1800 GMT).
Some 6.5 million people, about a third of the state's population, had been ordered to evacuate southern Florida.
Officials warned that Irma's heavy storm surge - seawater driven on land by high winds - could bring floods of up to 15 feet (4.6 m) along the state's western Gulf Coast. Small whitecapped waves could be seen in flooded streets between Miami office towers.
"There is a serious threat of significant storm surge flooding along the entire west coast of Florida," Governor Rick Scott told a press conference. "This is a life-threatening situation."
Tornadoes were also spotted through the region.
Irma is expected to cause billions of dollars in damage to the third-most-populous U.S. state, a major tourism hub with an economy that generates about 5 percent of U.S. gross domestic product.
About 1.8 million Florida homes and businesses had lost power, according to Florida Power & Light and other utilities.
The National Hurricane Center forecast that Irma's center eye will move near or over the state's west coast later on Sunday.
The storm killed 24 as it raged through the Caribbean. It has already claimed at least one life in Florida, a man found dead in his pickup truck, which had crashed into a tree in high winds.
MIAMI BUILDINGS SWAY, STREETS FLOODED
The storm winds downed a construction crane and shook tall buildings in Miami, which was about 100 miles (160 km) from Irma's core.
Deme Lomas, who owns Miami restaurant Niu Kitchen, said he saw a crane torn apart by winds and dangling from the top of a building.
"We feel the building swaying all the time," Lomas said in a phone interview from his 35th-floor apartment. "It's like being on a ship."
Waves poured over a Miami seawall, flooding streets around Brickell Avenue which runs a couple of blocks from the waterfront through the financial district and past consulates, leaving high rise apartment buildings standing like islands in the flood.
"There's water everywhere," said Chaim Lipskar, rabbi at the Rok Family Shul that is sheltering a few families through the storm. "It's up and down Brickell and all over the side streets."
South Florida's large population of elderly residents posed a severe test for the emergency shelters.
One woman in Miami's Little Haiti neighborhood delivered her own baby because emergency responders were not able to reach her, the city of Miami said on Twitter. The two are now at the hospital, it said.
Irma comes just days after Hurricane Harvey dumped record-setting rain in Texas, causing unprecedented flooding, killing at least 60 people and an estimated $180 billion in property damage. Almost three months remain in the Atlantic hurricane season, which runs through November.
U.S. President Donald Trump spoke to the governors of Alabama, Georgia, South Carolina and Tennessee on Sunday and issued a disaster declaration for Puerto Rico, which was hit by the storm last week, the White House said.
(Additional reporting by Sarah Marsh in Remedios, Marc Frank in Havana, Bernie Woodall, Ben Gruber and Andy Sullivan in Miami, Colleen Jenkins in Winston-Salem, North Carolina, Doina Chiacu and Roberta Rampton in Washington and Scott DiSavino in New York; Writing by Scott Malone; Editing by Ross Colvin and Andrew Hay)