The storm was about 530km east of Grand Turk Island packing maximum sustained winds of 205km/h, the NHC said on Sunday.
It had been gauged as high as a catastrophic Category 5 with maximum sustained winds of 240 kph, before being downgraded.
It had earlier been forecast to strengthen into this week.
The meteorological services of France and the Netherlands discontinued tropical storm watches for St. Martin, St. Barthelemy and Sint Maarten, the NHC said.
On Sunday, Erin was moving west-northwest at nearly 22 km/h with a decrease in forward speed expected and a turn to the north on Monday and Tuesday.
Erin was forecast to pass to the east of the Turks and Caicos islands and the southeastern Bahamas on Sunday night and Monday.
Swells generated by Erin will continue to affect parts of the northern Leeward Islands, the Virgin Islands, Puerto Rico, Hispaniola and the Turks and Caicos Islands for the next couple of days.
These swells will spread to the Bahamas, Bermuda, the east coast of the United States, and Atlantic Canada during the early and middle portions of the week.
Rough ocean conditions will likely cause life-threatening surf and rip currents, the NHC said.
The Bahamas, which provides some meteorological services for the Turks and Caicos Islands, issued a Tropical Storm Watch for the British islands to its southeast.
Erin has also raised concerns about wildfire risks if human-caused sparks ignite parched vegetation and strong dry winds fan the flames.
Senior meteorologist Andrew Siffert said these conditions could arise if Erin grows into a powerful offshore storm fueled by colliding warm and cold air rather than tropical seas.
Insurance-linked securities manager Twelve Securis said on Friday that Erin was forecast to remain far enough offshore to spare the US East Coast from significant impacts.
with AP
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