NEW ORLEANS — Tropical Storm Karen continued its slow trudge Saturday toward the Gulf Coast, threatening to bring heavy wind and high rains despite losing some of its punch.

Officials from Louisiana to northwest Florida acknowledged that the storm was weakening and sent some emergency workers home, but urged residents to be cautious.

“The storm’s weakened, and that’s good news, but we’re not out of the woods yet,” New Orleans Mayor Mitch Landrieu said at a news conference. He warned of likely high winds, street flooding and power outages.

The National Hurricane Center in Miami said forecasters had discontinued tropical storm watches across much of the Gulf Coast but that a portion of Louisiana remained under a tropical storm warning.

Karen stalled for several hours Saturday but began moving slowly northward at about 2 mph by the late afternoon. It had maximum sustained winds of 40 mph, making it a weak tropical storm.

Karen’s center was likely to come ashore either Saturday night or Sunday morning. It was expected to weaken further and lose tropical-storm status on Sunday.

Rick Knabb, the director of the National Hurricane Center in Miami, noted that “there is still the potential for some locally heavy rainfall and for some storm surge in coastal areas, but the magnitudes of those hazards greatly reduced. We still could see 1 to 3 feet of coastal flooding due to storm surge in some spots.”

In low-lying Plaquemines Parish, La., officials changed an evacuation order from mandatory to voluntary Saturday afternoon. More than 80 evacuees from the area, at the state’s southeastern tip, had taken refuge at a public shelter, which would remain open Saturday.

They gathered in an auditorium where they rested on cots, watched for weather updates on TV and chatted outside on the front steps.

“I don’t really know what to expect, but they told us to evacuate, so we got out,” said Dana Etienne, 27, of Phoenix, La., who was at the shelter with her three young children.

Ahead of the storm, squalls of rain hit workers sandbagging low sections of the flood-prone town of Lafitte, La., along Bayou Barataria.

“We have a high tide, but we only have another 15-17 hours to worry about, and I don’t think the tide will come up much more in that time,” Mayor Timothy Kerner said. “It looks like it might come up another foot or two, but I think we’re going to be OK.”

Coastal authorities closed flood gates along waterways that could be affected by tides driven by the storm.

In New Orleans, the U.S. Army Corps of Engineers continued closing barriers designed to keep surge out of the Inner Harbor Navigation Canal — scene of catastrophic flooding in 2005 when flood walls failed during Hurricane Katrina.

Col. Richard Hansen of the corps said more gates along various canals could be closed, and warned boaters not to get caught on the wrong side of those gates “If there is a gate in the system, it may not be open when you decide to come back in,” Hansen said. “So it’s time to pull your boats out of the water and quit fishing.”