A spokesman for the UK group said they would defend the right to continue using the name.
He said: "One Direction's management tried to resolve the situation amicably when the matter first came to light, but the Californian group has now filed a lawsuit claiming they own the name.
"One Direction's lawyers now have no choice but to defend the lawsuit and the band's right to use their name."
A spokeswoman for Syco declined to comment.
The Californian group, who say they have recorded two albums and gained a following in the US, have asked the British band to change their name after claiming they filed a trademark application for the use of the moniker One Direction.
The US One Direction are asking for:
- The British band to change their name.
- $1 million in damages.
- An injunction to stop Syco Entertainment and Sony Music from using the name in promotional material.
- A share of the profits earned by the British band.
The band's song "What Makes You Beautiful" became the highest debut single for a UK band in the US for almost 14 years, charting at 28 in the Billboard Singles Hot 100.
On their Facebook page the US group released a statement on the legal dispute saying: