The first tropical cyclone, first named storm, and first hurricane on the season, Abby developed over the northwestern Caribbean Sea on June 1, as a result of the interaction between a mid-tropospheric trough and a cold front.

Moving generally north-northeastward, the depression slowly strengthened while approaching the western tip of Cuba, becoming Tropical Storm Abby late on June 2.

The storm dropped heavy rainfall in western Cuba, with up to 12 inches (300 mm) on Isla de la Juventud.

Initially, Abby weakened slightly after moving inland, but then maintained intensity while tracking slowly eastward across Florida.

Satellite imagery indicated that the cold front and mid-tropospheric trough began merging as the low-level convergence field increased.

Thereafter, barometric pressures in the western Caribbean were decreasing as deep southwesterly flow caused very warm and moist air to enter the area.

At 0600 UTC on June 1, the system developed into Tropical Depression One, while situated about 55 miles (89 km) northeast of Guanaja, Honduras.

When a weak cold front moved into the area, it generated convection, gaining enough organization to be called a tropical depression on June 1.

The initial circulation was not embedded within the convection, but as it moved slowly north-northeastward, it was able to strengthen and become better organized, reaching tropical storm strength on the 2nd.

It crossed the western tip of Cuba, and upon reaching the southeast Gulf of Mexico Abby achieved hurricane strength.

Abby weakened to a tropical depression as it moved over Georgia, and over the next 6 days, it wandered around the Carolinas, finally dissipating on the 13th east of Virginia.

[1] At 2200 UTC on June 2, the Weather Bureau posted a gale warning from south of Tampa Bay to Melbourne on the east coast, including the Florida Keys and Lake Okeechobee.

[8] At 1900 UTC on June 6, the storm warning was discontinued at and south of St. Augustine, Florida, while the entire hurricane watch was canceled.

[12] In May, the United States Army Corps of Engineers (USACE) scheduled a mock preparation session for the 1968 Atlantic hurricane season.

[15] In Cuba, Abby dropped 12 inches (305 mm) of rain in Isle of Pines and wind gusts up to 50 mph were reported.