Thousands of Louisianans broke out sandbags or fled to higher ground on Thursday as Tropical Storm Barry threatened to turn into the first hurricane of the season and blow ashore with torrential rains that could pose a severe test of New Orleans’ improved post-Katrina flood defenses.

National guard troops and rescue crews in high-water vehicles took up positions around the state as Louisiana braced for the arrival of the storm along its swampy southern tip Friday night or early Saturday.

Barry could have winds of about 75mph (120km/h), just barely over the 74mph threshold for a hurricane, when it comes ashore, making it a category 1 storm, forecasters said.

But it is expected to bring more than a foot and a half (45cm) of rain in potentially ruinous downpours that could go on for hours as the storm passes through the metropolitan area of nearly 1.3 million people and pushes slowly inland.

Officials in New Orleans itself declined to issue evacuation orders, instead recommending on Thursday that residents “shelter in place”, store up several days of supplies, and move vehicles to higher ground.

Barry is expected to turn into the first hurricane of the season by Friday, coming ashore along the Louisiana-Mississippi-Texas coastline and pouring more water into the already swollen Mississippi River.

Forecasters said the biggest danger in the days to come is not destructive winds but heavy rain as the slow-moving storm makes its way up the Mississippi valley.

Louisiana’s governor, John Bel Edwards, declared an emergency and said national guard troops and high-water vehicles will be positioned all over the state.

“The entire coast of Louisiana is at play in this storm,” he warned.

A spokesman for the army corps of engineers in New Orleans said the agency is not expecting widespread overtopping of the levees, but there are concerns for areas south of the city. Mandatory evacuations were ordered for people living near the Mississippi River in Plaquemines parish, at Louisiana’s south-eastern tip, as well as the gulf barrier island of Grand Isle.

The National Weather Service expects the river to rise to 20ft (6 meters) by Saturday morning at a key gauge in the New Orleans area, which is protected by levees 20 to 25ft high.

“We’re confident the levees themselves are in good shape. The big focus is height,” a corps spokesman, Ricky Boyett, said. In St Bernard parish on Thursday morning, crews fortified earthen levees with dump trucks full of soil.

Forecasters said Louisiana could see up to 12in of rain by Monday, with isolated areas receiving as much as 18in.

And the storm’s surge at the mouth of the Mississippi could also mean a river that has been running high for months will rise even higher.

Residents sit under a bus shelter along a flooded Broad Street as heavy rain falls in New Orleans on 10 July. Photograph: David Grunfeld/AP

New Orleans got an early taste on Wednesday of what may be in store. Floodwaters invaded downtown hotels and businesses and turned streets into rivers, paralyzing rush-hour traffic and stalling cars. Some people paddled their way around in kayaks.

The city’s sewerage and water board said the pumping system that drains the streets was at full capacity. But the immense amount of rain in three hours would overwhelm any system, said the agency’s director, Ghassan Korban.

As the water from Wednesday morning’s storms receded, people worried about what might come next.

Tanya Gulliver-Garcia was trying to make her way home during the deluge. Flooded streets turned a 15-minute drive into an ordeal lasting more than two hours.

“This is going to be a slow storm,” she said. “That’s what I’m concerned about.”