NASHUA — Minnesota Representative Michele Bachmann held aloft a tea bag at a GOP fund-raiser in a Nashua hotel yesterday, drawing loud approval for the reference to the Tea Party movement and its inference of revolution.

But at an earlier event in Manchester, N.H., Bachmann, one of the Tea Party’s shining lights in Congress who is considering a run for president, appeared to show major gaps in her grasp of the Revolutionary War.

“You’re the state where the shot was heard around the world in Lexington and Concord,’’ Bachmann told a group of conservative lawmakers and students at a Manchester school. “And you put a marker in the ground and paid with the blood of your ancestors the very first price that had to be paid to make this the most magnificent nation that has ever arisen in the annals of man in 5,000 years of recorded history.’’

The “shot heard ’round the world’’ may have echoed in New Hampshire, but it was, of course, fired in Massachusetts.

The gaffe was reported yesterday on the website RealClearPolitics. According to the site, Bachmann, later in the same speech, referenced the battles a second time without correcting her error.

The remark demonstrated a surprising lack of command of the basic facts of the historic events from which the Tea Party movement derives its name and is likely to go down as one of the bigger missteps of the early primary season.

“Honestly, when she did it, everybody looked around, obviously, and was like ‘uh oh,’ but she carries herself in such a professional way — they’re all legislators in that room, and every single one of them has made the exact same mistake, maybe not on the same topic,’’ said Andrew Hemingway, chairman of the Republican Liberty Caucus of New Hampshire, which organized the event, in a phone interview. “When you’re speaking publicly that much, you’re going to make mistakes and say, ‘I know better.’ ’’