The American group — who are also a five-piece — is demanding a court order to force Niall Horan, Zayn Malik, Liam Payne, Harry Styles and Louis Tomlinson to change the name of their band.
In legal papers, the Americans claim they formed in 2009 — before the X-Factor boys had even met.
They also say they were first in filing a trademark application at the US Patent and Trademark Office.
And they are demanding three times the profits made by the Brits, as well as damages of more than £600,000.
A blog by the US band said they liked the Brit act but added: “To protect our rights, we reluctantly have filed a lawsuit.”
In an online message to their fans, they explained: “Despite our best efforts, we were unable to negotiate a reasonable compromise with the handlers for the band.”
The group said their rivals had known about their claim to the name since the spring of 2011.
The US lads said: “They chose not to use a different name. They chose to press ahead, using the exact same name, One Direction, setting up the current difficulties and confusion in the United States.”
The blog added: “The British boy band is well funded and high profile. They have Mr Cowell’s enormous resources behind them. We on the other hand do not.
“In our view, we were here first. We have rights. We have talent, and we have heart. We are standing up for all of the above. Not having money does not take away your rights or make you ’less than’.”
They wished the UK act well and added: “We wonder if they even know what their handlers are up to.”
The legal action was revealed as Harry and the boys enjoyed Stateside success — landing a No1 with their debut album Up All Night.
Meanwhile the Californian One Direction — led by singer and pianist Sean O'Leary — have made little impact, with their biggest gigs being at local fairs and bars.
Fans from all over the world have taken to Twitter to support the British and an online petition has been launched.
One fan tweeted: "It's not our fault that US One Direction faded away. Leave our UK boys alone."
It is not the first time one of Simon Cowell’s X Factor bands has run into trouble over a name.
Last year’s show winners Little Mix had to change their name from Rhythmix, which was also the name of a Brighton-based charity.
The American One Direction have recorded two albums but on their iTunes page one customer wrote: "NOT X FACTOR 1D!!
"I thought this was the british 1D from xfactor 2010 dang it."
Below that another post, under the heading, 'THIS IS SOOOO AWESOME!!!' sings the US band's praises.
It says: "I originally thought this was the UK One Direction, but then i got to listen, and i realized this wasnt. these guys are really great as well! i would definatly buy this album! these guys deserve it!"