HOUSTON — Harvey intensified into a hurricane Thursday and steered for the Texas coast with the potential for up to 3 feet of rain, 125 miles-per-hour winds, and 12-foot storm surges in what could be the fiercest hurricane to hit the United States in almost a dozen years.

Forecasters labeled Harvey a ‘‘life-threatening storm’’ that posed a ‘‘grave risk.’’ Millions of people braced for a prolonged battering that could swamp dozens of counties more than 100 miles inland.

Landfall was predicted for late Friday or early Saturday between Port O’Connor and Matagorda Bay, a 30-mile stretch of coastline about 70 miles northeast of Corpus Christi. The region is mostly farm or ranchland dotted with waterfront vacation homes and has absorbed numerous Gulf of Mexico storms for generations.

Harvey grew unexpectedly quickly Thursday from a tropical depression into a Category 1 hurricane. Fueled by warm Gulf waters, it was projected to become a major Category 3 hurricane. The last storm of that category to hit the United States was Hurricane Wilma in October 2005 in Florida.

Superstorm Sandy, which pummeled New York and New Jersey in 2012, never had the high winds and had lost tropical status by the time it struck. But it was devastating without formally being called a major hurricane.

‘‘We’re forecasting continuing intensification right up until landfall,’’ National Hurricane Center spokesman Dennis Feltgen said.

Typical Category 3 storms damage small homes, topple large trees, and destroy mobile homes. As in all hurricanes, the wall of water called a storm surge poses the greatest risk.

Harvey’s effect would be broad. The hurricane center said storm surges up to 3 feet could be expected as far north as Morgan City, La., some 400 miles away from the anticipated landfall.

And once it comes ashore, the storm is expected to stall, dumping copious amounts of rain for days in areas like flood-prone Houston, the nation’s fourth most-populous city, and San Antonio.

National Weather Service director Louis Uccellini said scientists were ‘‘looking at a potentially impactful storm over a two-, three-, four-day period.’’

No widespread evacuations were immediately ordered. Officials in Port Aransas and Aransas Pass, two small coastal towns near the projected landfall area, asked the 12,000 residents to leave and warned those who stayed behind that no one could be guaranteed rescue. ‘‘We are closing down,’’ said Bethany Martinez, a front desk clerk at a Holiday Inn Express at Port Aransas. The 74-room hotel a couple of blocks from the Gulf of Mexico was about two-thirds full before all guests were cleared out.

This would be the first hurricane for Martinez, who is pregnant and has two boys, 5 and 6. They were with grandparents in Austin. Asked about her demeanor, she replied: ‘‘Afraid.’’

Harvey would be the first significant hurricane to hit Texas since Ike in September 2008 brought winds of 110 miles per hour to the Galveston and Houston areas and inflicted $22 billion in damage. It would be the first big storm along the middle Texas coast since Hurricane Claudette in 2003 caused $180 million in damage.

It’s taking aim at the same vicinity as Hurricane Carla, the largest Texas hurricane on record. Carla came ashore in 1961 with wind gusts estimated at 175 miles per hour and inflicted more than $300 million in damage. The storm killed 34 people and forced about 250,000 people to evacuate.

President Trump on Twitter asked people to get ready for the hurricane and posted links to websites for the Federal Emergency Management Agency, the National Hurricane Center, and a Homeland Security site with tips for emergency preparedness.

Many people heeded the warnings.

In Houston, one of the nation’s most flood-prone cities, Bill Pennington was philosophical as he prepared his one-story home for what he expected would be its third invasion of floodwaters in as many years and the fifth since 1983.

‘‘We know how to handle it. We’ll handle it again,’’ Pennington said he told his nervous 9-year-old son.

Dozens were in lines early Thursday at a Corpus Christi Sam’s Club, at home improvement stores and supermarkets. The city also was passing out sandbags.

Alex Garcia bought bottled water, bread, and other basics in the Houston suburb of Sugar Land after dropping his daughter off at college. He said grocery items were likely more available in Houston than back home in Corpus Christi, where Garcia, a beer distributor salesman, said stores were ‘‘crazy.’’