Employee lying to me about other employees

I'm a manager and I often have a employee who will lie to me about other employees. They will say that "someone is mad that we are getting pressure to get this task done by a certain date", when I speak with the person that is "mad" to understand why they are upset they say that they were never mad, that the employee who spoke to me was the person that was mad. They make up lies about other employees to their coworkers. I cannot trust what they tell me, and it is ruining the morale of the team because they also can't trust them. They twist my words when speaking with coworkers. I often have to clear the air and have frequent conversations with the employee and co-workers.

How would you approach this situation?