Tropical Storm Lee is drenching New Orleans as the southern city, inundated by Hurricane Katrina in 2005, faced a test of its flood defences from the slow-moving system.

Rainfall topped 30cm in parts of the New Orleans metropolitan area. The storm was inching toward the marshy Louisiana coast and was forecast to dump up to 51cm of rain to southeast Louisiana over the next few days.

The storm centre was about 137km west-southwest of Morgan City, with maximum winds of 80km/h. Winds were expected to stay below the 119km/h threshold of hurricane strength as the storm crawls ashore.

In New Orleans the storm evoked memories of Hurricane Katrina, which flooded 80% of the city, left 1,500 people dead and caused more than $80bn in damage.

Half the city, a major US tourist destination, lies below sea level and is protected by a system of levees and flood gates.

The levees had pumped away about 20cm of rain so far, with isolated reports of flooding in roads and homes. The system can process about 2.5cm of rainfall per hour, but the storm's slow-moving nature remained a worry, officials said.

"Don't go to sleep on this storm," Mayor Mitch Landrieu told residents, warning stormy conditions could continue for the next 36 hours.

New Orleans is under a flash flood watch through Monday night due to heavy rain potential, the National Weather Service said.

Potential damage from wind gusts up to 80km/h will also be a concern for New Orleans today as Lee's centre moves inland, it said.

No injuries or deaths were reported in Louisiana, but rough waters off Galveston Island in Texas led to the drowning death of a 34-year-old man, an island official said.

Lee's tidal surge could spur coastal flooding in Louisiana, Mississippi and Alabama before drenching a large swath of the southeast and Appalachian regions next week.

Hurricane Katia upgraded to category 2 storm

Separately, Hurricane Katia strengthened rapidly over the open Atlantic today, bulking up to a category 2 storm, the US National Hurricane Center said.

Katia had top sustained winds of 160km/h, the Miami-based hurricane centre said.

It said it was still too soon to gauge the potential threat to land or the US east coast from the storm, which could become a "major" hurricane with maximum sustained winds of at least 178km/h tomorrow.