"Depression Becomes the Sixteenth Named Storm of the Season Over the Open Atlantic," the weather agency said on Twitter.
The storm is moving northwest at the speed of 15 miles per hour, packing gale winds of up to 40 miles per hour, according to NHC.
"Rainfall around the southern periphery of Tropical Storm Peter may lead to areas of urban and small stream flooding from late Sunday into Tuesday across Puerto Rico, the Virgin Islands, and the Northern Leeward Islands," the agency said.
The Atlantic hurricane season runs from 1 June to 30 November, peaking in early September. On Tuesday, tropical storm Nicholas swept the United States' southeastern coastline, causing President Joe Biden to declare a state of emergency in Louisiana.