Empathic statements are critical to effective negotiation. They allow us to transcend the freeze, flight or fight response of the more primitive parts of our brain (the Limbic System) and get into the executive function of problem-solving (pre-frontal cortex). This is how we "step in another's shoes" or imagine how to experience the opposition's reality as they do, and acknowledge that reality. You do not have to agree or make a concession but you will be less persuasive if you don't acknowledge people's positions. This is a pillar of hostage and terrorist negotiation expert Chris Voss' methodology, but it applies to virtually every human and human condition.
Consider approaching a car salesman. You: "I just heard that customer storm off because they were offended by your counter. It must be difficult to determine if a buyer is serious or they are just haggling for sport." Car Salesman: "Part of the job, but it can be frustrating." You: "What is the best way you work with people to disclose all issues and feel like you are being dealt with respectfully." Car Salesman: "When they tell me exactly what they want and range in their budget, and let me work within those constraints." You: "So you like them to tell you their constraints in their purchase decision upfront?" Car Salesman: "That's right."
Imagine you sitting across the table on the other side of the transaction. What are their fears, hopes, and dreams of that person? Then say them out loud. If you don't have time to paraphrase, Voss simply recommends you repeat or verbally mirror the last three words the opposition says. This transcends the primitive parts of their brain that may impede your effectiveness. When used on you, know it and send it back as well. This is typical among professionals.