Hurricane Irma has killed at least 10 people in Cuba over the weekend, the authorities say, bringing the death toll in the Caribbean to 38 as the weakened storm moves up the US state of Florida.

Cuba's civil defence authorities said in a statement on Monday that the victims perished due to various causes such as accidents, collapsed buildings and not heeding orders to evacuate in the four provinces of Havana, Matanzas, Sancti spiritus and Ciego de Avila.

Irma, which was downgraded to a tropical storm on Monday, is centred about 170km north-northwest of Tampa area of Florida, with sustained winds of about 110km/h as of 9:00 am local time (13:00 GMT).

Warnings of dangerous storm surges remained in effect through vast swaths of peninsular Florida, where more than six million people had been ordered to flee Irma in one of the biggest evacuations in US history.

"As little as six inches of moving water can knock you down," tweeted the state's governor Rick Scott following the downgrade.

Irma was churning towards the heavily populated Tampa Bay region, a zone seen as particularly susceptible to storm surges due to its geographical position and sloping land off the coast.

The storm had killed three people when it struck the southern Florida Keys island chain as a more powerful Category Four on Sunday.

"There's a huge difference between a (Category) 3 and 5 when it makes landfall," said private meteorologist Ryan Maue of WeatherBell Analytics "Barbuda is an example of that. It was wiped."

"This is obviously not the worst case scenario for Florida overall," Maue said. Had the centre of Irma hit Florida 32-50 kilometres to the east "it would have been much worse".

READ MORE: What you need to know - Hurricane Irma and its impacts

Irma, which was expected to cause billions of dollars in damage to the third-most-populous US state, it hit just days after the Houston area was deluged by unprecedented flooding from Hurricane Harvey, which dumped more than 127cm of rain in parts of Texas.

Harvey killed at least 60 people and caused an estimated $180bn in property damage.

US President Donald Trump, acting at the governor's request, approved a major disaster declaration for Florida on Sunday, freeing up emergency federal aid in response to Irma, which he called "some big monster".