The Japanese attach great importance to harmony in human relationships. So we tend to avoid refusing offers or invitations sharply because it might damage our relationships with others.
For example, when you are offered some kind of food you don't like, you first of all show appreciation to the other person's offer by saying Arigatô gozaimasu, meaning "Thank you very much." And then you can refuse the offer using an evasive answer such as Chotto..., meaning "Er…". This chotto is a very useful expression because you can use it not only for calling someone but also for refusing something.
Euphemistic expressions are often used in business situations. An expression that is frequently used to refuse a business deal with a client is Kentô shitemimasu. Although Kentô shitemimasu basically means "I will consider," it implies the nuance of "Please don't expect a good answer."