Flossie, with maximum sustained winds of 40 mph, was about 80 miles north-northwest of Hilo and 145 miles east of Honolulu, traveling west-northwest at 18 mph, the National Weather Service Central Pacific Hurricane Center in Honolulu said in its 2 p.m. HST advisory.
A tropical storm warning was posted for the islands of Oahu, Hawaii, Maui, Molokai, Lanai and Kahoolawe.
A tropical storm watch was in effect for Kauai and Niihau.
Flossie was expected to continue moving west-northwest over the next 24 to 48 hours.
Some weakening is forecast during the next two days, forecasters said.
Flossie was expected to bring heavy rain over the warning area through Monday night. Rainfall totals of 4 to 10 inches were possible, with isolated amounts of 12-15 inches, forecasters said.
Rainfall could cause life-threatening flash floods and mudslides, the hurricane center said.
Flossie was expected to generate dangerously high surf into Tuesday for east-facing shores of Hawaii, the Big Island.
Hawaii County Mayor Billy Kenoi said non-essential workers were to stay home Monday, the Honolulu Star-Advertiser reported.
Maui Mayor Alan Arakawa closed county parks and offices.
Kenoi and Hawaii Gov. Neil Abercrombie issued emergency proclamations.