Juliette was about 95 miles northwest of Cabo San Lucas, Mexico, traveling northwest at 23 miles per hour, the National Hurricane Center in Miami said in its 2 a.m. EDT advisory.
Maximum sustained winds were 50 miles per hour with higher gusts.
A tropical storm warning was issued by the Mexican government for the coast of Baja California from San Evaristo to Bahia Magdalena, including Cabo San Lucas.
Juliette was expected to show a reduction in forward speed over the next 24 hours as the storm turns toward the west-northwest, with an additional decrease in forward speed and some weakening Thursday night.
Rainfall of 1 to 3 inches could be expected along the southern part of Baja California.
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