The California based rock band are suing the British and Irish outfit of the same name, claiming they own the rights to the name In America, and have vowed not to be swayed by the power of their record company, Syco and its parent label, Sony Music.
Dan O'Leary, who manages the US group, told The Sun newspaper: ''I don't care how powerful Simon Cowell is. He's mad if he thinks we're going to lie down, sit down or back down over this - whatever power and money he has behind him.
''The British One Direction 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.''
The US One Direction - fronted by Dan's son, Sean O'Leary - have filed a copyright infringement claim in California, seeking three times the profits earned by the UK based band and $1 million compensation.
Their lawsuit claims the UK group's record companies were aware of the fact the two bands had the same name as early as 2011 but chose to ignore this fact.
Dan added: ''It's black and white what's been done. We asked Simon Cowell to change their name before they came here. But they ignored us, and now we're reluctantly at this point of legal action.''
He said: ''There should be plenty of room for both bands to grow and thrive. We hope that this dispute will be resolved soon, and then all of us can focus on what we do best - making music.''