Tropical Storm Idalia, which formed on Sunday, was expected to strengthen to a Category 2 hurricane by the time it reaches Florida’s Gulf Coast on Tuesday in what forecasters said would be a “very significant and impactful hurricane.”

Winds were predicted to reach a peak of 100 miles per hour, Jamie Rhome, deputy director of the National Hurricane Center, said in an update on Sunday evening.

“Evacuations may be necessary for this storm later today or tomorrow,” Mr. Rhome said.

“The hazards absolutely will extend beyond the cone,” he added, referring to the forecast maps showing the storm’s potential path. “Do not focus exclusively on the cone to determine your risk.”

Idalia, the latest named storm of the 2023 Atlantic hurricane season, also threatens to bring heavy rains to Georgia and the Carolinas, forecasters said.

A hurricane watch was issued for a large section of western Florida, extending from Englewood to Indian Pass, and including Tampa Bay, officials said.

A tropical storm watch was also issued from the Gulf Coast south of Englewood, which is about 80 miles south of Tampa, to Chokoloskee, a community roughly 65 miles south of Fort Myers, while a storm surge watch was in effect from Chokoloskee to Indian Pass.

The Florida Division of Emergency Management told residents to keep their gas tanks at least halfway full in case emergency evacuation orders were issued.

Gov. Ron DeSantis of Florida signed an executive order on Saturday declaring a state of emergency in 33 counties in preparation for the storm.

“If you are in the path of this storm, you should expect power outages, so please prepare for that,” he said on Sunday. “If you are power-dependent — particularly people who are elderly or who have medical needs — please plan on going to a shelter.”

The state mobilized 1,100 members of the National Guard, which has 2,400 high-water vehicles and 12 aircraft ready for rescue efforts. Electric companies will have workers on standby starting on Monday.

The Hurricane Center noted in an advisory on Sunday that from Tuesday into Wednesday, parts of the west coast of Florida, the Florida Panhandle and southern Georgia could get up to six inches of rain, with higher isolated totals of 10 inches.

Heavy rainfall was also expected to spread into portions of the Carolinas Wednesday into Thursday, the center said.

“Rainfall may lead to flash and urban flooding, and landslides across western Cuba,” the center said. “Scattered flash and urban flooding can also be expected across portions of the west coast of Florida, the Florida Panhandle and portions of the Southeast U.S. by Tuesday into Thursday.”

On Sunday night, Cuba issued a hurricane warning for Pinar Del Rio, a city located a two-hour drive west of the country’s capital, Havana. The Cuban government also upgraded a tropical storm watch for the Isle of Youth to a tropical storm warning.

A tropical storm warning was issued for the Dry Tortugas islands, which had previously been under a watch advisory, and a watch was in effect for Lower Florida Keys West, west of the Seven Mile Bridge, the center said on Sunday night.

The combination of the tide and storm surge was expected to bring water levels up to 11 feet in some parts of the Florida coast, forecasters said.

The storm had maximum sustained winds of 60 m.p.h and was 145 miles south of the western tip of Cuba on Sunday night. It was expected to move over the Gulf of Mexico on Monday and strengthen to a hurricane by Tuesday, as it approaches Florida.

The west coast of Florida has been no stranger to hurricanes in the past several years.

Hurricane Ian in 2022 and Hurricane Michael in 2018 caused extensive damage from strong winds and storm surges after moving out of the Caribbean and rapidly intensifying in the Gulf of Mexico before striking Florida as major hurricanes.

There were 14 named storms last year, after two extremely busy Atlantic hurricane seasons in which forecasters ran out of names and had to resort to backup lists. (A record 30 named storms took place in 2020.)

There is consensus among scientists that hurricanes are becoming more powerful because of climate change. Although there might not be more named storms overall, the likelihood of major hurricanes is increasing.

Climate change is also affecting the amount of rain that storms can produce. In a warming world, the air can hold more moisture, which means a named storm can hold and produce more rainfall, like Hurricane Harvey did in Texas in 2017, when some areas received more than 40 inches of rain in less than 48 hours.

Orlando Mayorquin contributed reporting.