JACKSONVILLE, Fla. (AP) — Tropical Storm Fay will likely not become a hurricane, forecasters said Wednesday, relieving fears the zig-zagging storm would return from the Atlantic with punishing force later this week.

However, the storm continued to plod up the peninsula with the possibility of dumping up to 20 inches of rain in some areas — good news for parched farmland in northern Florida and much of Georgia, but bad for flood-prone areas in both states.

‘‘It’s very seldom we’re hoping for a hurricane, but we are,’’ said Randy Branch, a farmer in southeast Georgia where lingering drought has left about a third of his cotton and peanut crops bare this summer. ‘‘We need some rain pretty bad.’’

The storm hit the Florida Keys on Monday, veered over the Gulf and then traversed east across the state Tuesday on a path that would have taken it over the Atlantic before it curved toward the Florida-Georgia border.

Forecasters had originally expected Fay to get a dose of energy when it moved over the ocean and possibly become a hurricane. But the storm’s center remained just inland early Wednesday and forecasters said it may not go over the water until the afternoon.

There were no new reports of damage Wednesday and only minor street flooding in the Melbourne area, where Fay was predicted to dump between 6 and 12 inches of rain.

A hurricane watch was discontinued for parts of north Florida and Georgia. A tropical storm warning was extended, covering an area from Fort Pierce to Altamaha Sound in Georgia. A warning means such conditions are expected within 24 hours, while a watch means such conditions are possible within 36 hours.

The storm was near Cape Canaveral at 11 a.m. EDT Wednesday. Its maximum sustained winds were back up to about 50 mph and it was moving north at about 3 mph.

National Weather Service meteorologist Steve Letro said it’s possible southern Georgia could receive 10 to 20 inches of rain — enough to cause severe flooding — if it makes a second landfall.

‘‘I know people hate drought, but when you’re talking about a tropical cyclone relieving drought conditions, be careful what you wish for,’’ said Letro, the chief meteorologist in Jacksonville, Fla.

In Duval County, which surrounds Jacksonville, officials prepared shelters, cleared drainage areas that could flood and readied emergency response teams. Public schools canceled Wednesday and Thursday classes, and mobile home residents were encouraged to find sturdier shelter.

‘‘Our biggest concern is complacency. Jacksonville has a history of being shielded from storm systems. While we don’t want anyone to panic, we want everyone in the area to take this storm seriously,’’ said Misty Skipper, a county spokeswoman.

Business was brisk at Jacksonville grocery stores and gas stations as people prepared for Fay’s arrival. Velton Jones, manager at a discount department store, said he was selling basics such as water, flashlights, emergency supplies and cigarettes.

‘‘The storm’s coming, people want to have their cigarettes,’’ Jones said. ‘‘I expect it’s going to be chaotic in here today.’’

In southeast Georgia, Camden County public works crews cleaned storm drains and ditches in preparation for possible flooding. The Georgia Emergency Management Agency also began 24-hour operations Tuesday afternoon to monitor the storm.

A National Hurricane Center forecast late Tuesday projected that the storm’s path would take it through Alabama over the weekend. However, projections varied widely, prompting some in South Carolina to hope for crop-sating rain.

‘‘I just came in from the fields. Everything is burning up,’’ said Belton, S.C., farmer Charles Campbell. ‘‘If a storm is brewing down there, just send it up I-26.’’

Fay formed over the weekend in the Atlantic and was blamed for 20 deaths in the Caribbean before hitting Florida’s southwest coast, where it fell short of predictions it could be a Category 1 hurricane when it came ashore.

The storm flooded streets in Naples, downed trees and cut power to some 95,000 homes and businesses in South Florida. The worst of the storm’s wrath appeared to be 51 homes hit by a tornado in Brevard County, southeast of Orlando, including nine homes that were totaled.

Two injuries were reported in the Brevard County tornado, and a kitesurfer who was caught in a gust of wind Monday was critically injured when he slammed into a building in front of the beach near Fort Lauderdale. Kevin Kearney, 28, was still in critical condition Tuesday, Broward General Medical Center officials and his family said.