Maximum sustained winds increased to 150 miles per hour (241 kph) before nightfall, and forecasters said up to 18 inches (46 centimetres) of rain could fall.
On Twitter, President Donald Trump urged coastal residents to heed officials.
The NHC said on August 27 that the storm surge could penetrate up to 40 miles inland, and that floodwaters would not fully recede for several days.
Television footage showed heavy rain and strong winds lashing the south-western coastal city of Lake Charles in Louisiana.
As of NOAA's 4am update, Laura was packing 120mph winds and was moving toward the north near 15 miles per hour (24 km/h).More news: Scott Morrison takes on China amid rising concern over espionage
As Laura moved over land, it lost some energy and was downgraded in strength. Now more than 290,000 customers are without power in Louisiana (231,944) and Texas (61,153).
The damage was observed in Lake Charles, which is about 45 miles (72 kilometers) north of where the storm made landfall in Cameron early Thursday.
As of 8 p.m. CT, the Louisiana Department of Transportation and Development announced that part of Interstate 10 was closing ahead of Hurricane Laura. An extreme wind warning has been extended until 5 a.m. ET.
Earlier Wednesday, officials in Austin said the city had run out of free hotel rooms for evacuees and had started to send families fleeing the storm to a shelter almost 200 miles (322 kilometers) farther north.
Reports of damage in Lake Charles include damage to hotels, skyscrapers and to the Golden Nugget Casino.
Laura's eye hit a stretch of Louisiana near the Texas state line early Thursday as a Category 4.
The extreme wind warning in the area has been extended until 4 a.m. Lake Charles has seen sustained winds of 100 mph for nearly an hour.More news: Trump wants Biden to take 'drug test' before first debate
The storm's power has raised fears of a six-metre (20-foot) storm surge capable of sinking entire communities on the coast. Associated Press contributors include John L. Mone in Port Arthur, Texas; Gerald Herbert in Lake Arthur, Louisiana; Paul J. Weber in Austin, Texas; Seth Borenstein in Kensington, Maryland; Juan A. Lozano in Houston; Jake Bleiberg in Dallas; Jay Reeves in Birmingham, Alabama; Jill Bleed in Little Rock, Arkansas; Julie Walker in NY and Sophia Tulp in Atlanta.
Many residents of the city have been evacuate however there are some that remain in the city.
Half a million residents have been told to leave parts of Texas and Louisiana.
Appearing on Fox News on Wednesday Mr Abott said: "All the people who could potentially lose their life, if they know - number one in a hurricane - that's to make sure that you save your own life". "With four kids and 100 farm animals, it's just hard to move out", he said.
Victoria Nelson with her children line up to board a bus to evacuate Lake Charles.
The hurricane has been tapping into the favourable Gulf waters, and is still set to strengthen even more so, as a Category 4 storm, before making landfall near the Louisiana-Texas border Wednesday night or Thursday morning.More news: Anushka Sharma and Virat Kohli expecting first child in January 2021