HOUSTON — With time running out, tens of thousands of people fled Friday from the path of an increasingly menacing-looking Hurricane Harvey as it took aim at a wide swath of the Texas Gulf Coast that includes oil refineries, chemical plants and dangerously flood-prone Houston, the nation’s fourth-largest city.

Texas Gov. Greg Abbott warned that the monster system would be “a very major disaster,” and the forecasts drew fearful comparisons to Hurricane Katrina, one of the deadliest ever to strike the U.S.

“We know that we’ve got millions of people who are going to feel the impact of this storm,” said Dennis Feltgen, a spokesman and meteorologist for the National Hurricane Center. “We really pray that people are listening to their emergency managers and get out of harm’s way.”

The outer bands of the Category 3 storm arrived Friday, with rain pelting the coast, water levels rising and winds accelerating. Landfall was predicted for late Friday or early Saturday near Rockport, a fishing-and-tourist town about 30 miles northeast of Corpus Christi.

If it does not lose significant strength, the system will come ashore as the fiercest hurricane to hit the U.S. in nearly a dozen years.

Aside from the winds of 125 mph (201 kph) and storm surges up to 12 feet (4 meters), Harvey was expected to drop prodigious amounts of rain — up to 3 feet. The resulting flooding, one expert said, could be “the depths of which we’ve never seen.”

Galveston-based storm surge expert Hal Needham said forecasts indicated that it was “becoming more and more likely that something really bad is going to happen.”

At least one researcher predicted heavy damage that would linger for months or longer.

“In terms of economic impact, Harvey will probably be on par with Hurricane Katrina,” said University of Miami senior hurricane researcher Brian McNoldy. “The Houston area and Corpus Christi are going to be a mess for a long time.”

Before the storm arrived, home and business owners raced to nail plywood over windows and fill sandbags. Steady traffic filled the highways leaving Corpus Christi, but there were no apparent jams. In Houston, where mass evacuations can include changing major highways to a one-way vehicle flow, authorities left traffic patterns unchanged.

Federal health officials called in more than 400 doctors, nurses and other medical professionals from around the nation and planned to move two 250-bed medical units to Baton Rouge, Louisiana. Other federal medical units are available in Dallas.

Just hours before the projected landfall, the governor and Houston leaders issued conflicting statements on evacuation.

After Abbott urged more people to flee, Houston authorities told people to remain in their homes and recommended no widespread evacuations. Mayor Sylvester Turner on Friday tweeted “please think twice before trying to leave Houston en masse.” The spokesman of emergency operations in Harris County was even more direct, tweeting: “LOCAL LEADERS KNOW BEST.”