Hi - my name is XXXXX XXXXX I'm an Intellectual Property litigation attorney. Thanks for your question, and I'll be glad to assist you.
Domain names can be the source of trademark infringement claims if the domain name could confuse a customer and make him/her believe that one company is actually the other. But for this to be an issue, you would likely have to be in the same trade/business.
Here's a good article that you can read on this issue: http://www.nolo.com/legal-encyclopedia/avoid-trademark-infringement-domain-name-29032.html
If the domain name was being used before you began your business, this would be really difficult for you because they came first. But, if the domain name came after your business, then you would have a shot if you can prove that you're losing customers or that customers are confusing one business for another.
The best resolution is if you could work out a deal with the other company and try to settle because tradeXXXXX XXXXXtigation is expensive and protracted. Plus, there are a few issues with your situation that could be difficult to overcome. So, if you can work something out in good faith, that's probably the best way to proceed.
I hope this answers your question, but if you need something further, please don't hesitate to ask. Thanks!