Veracruz state officials said in a statement Friday that the storm could cause landslides and urged people living below hills and slopes to be prepared to evacuate.
Katia, a category one hurricane, was around 195 miles northeast of Veracruz at 12:00 GMT Thursday - with sustained winds of 80 miles (129 kph) per hour and gusts of 96 mph (154 kph), according to the National Meteorological Service of Mexico.
NHC noted that risky storm surge will raise water levels by as much as 5 to 7 feet above normal tide levels near and to the north of where Katia makes landfall.
The storm is expected to make landfall in Mexico's southeast coast late Friday or early Saturday.
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The SMN has called on populations to take extreme caution due to rain, wind, and flooding in the states of Veracruz, Puebla, San Luis Potosi, Hidalgo, Tlaxcala, Oaxaca, Chiapas and Tabasco. Rainfall between two and five inches is also possible over southern Tamaulipas, eastern San Luis Potosi, western Hidalgo, eastern Queretaro and southern Veracruz through Saturday evening.
But it was still expected to bring life-threatening floods and storm surge off the Gulf, though the extent of the storm's impact was unclear in the dark of night.
It was moving west-southwest at 11 kilometers per hour, and was projected to pour 10 to 15 inches of rain over northern Veracruz, eastern Hidalgo and Puebla. The storm was expected to weaken rapidly over the next day, the NHC said.