Hundreds of people fled the Bahamas island of Great Abaco by boat on Friday and thousands more tried to get on a cruise ship leaving neighbouring Grand Bahama to escape the catastrophic aftermath of Hurricane Dorian.

The most powerful hurricane on record to hit the Bahamas swept through the islands earlier this week, levelling entire neighbourhoods and knocking out key infrastructure, including airport landing strips and a hospital.

Hundreds, if not thousands, are still missing in the country of about 400,000 people, and officials say the death toll, which stands at 30, is likely to soar as more bodies are discovered in the ruins and floodwaters left behind by the storm.

In Freeport, witnesses said thousands crowded the port to try to get on a Bahamas Paradise Cruise Line ship offering free passage to Florida to those with necessary U.S. immigration documentation.

"People are desperate to leave, many homes simply gone," tweeted chef Jose Andres, whose World Central Kitchen relief organization landed in Freeport on Friday and began serving thousands of hot meals.

A boat with 250 evacuees left battered Abaco and arrived in Nassau, the capital of the Bahamas, which is located on New Providence island to the west and was less affected. Another with hundreds aboard was on its way, National Voice of the Bahamas radio reported, citing a spokesman for the country's National Emergency Management Agency (Nema).