Is it possible to act hard with the Client if he does not pay?

I wonder your opinion. We have one project, a website for the sale of real estate in a residential complex. We received 50% prepayment, completed the project, the client accepted the site. The question remains 50% of the final payment for the work. We correspond with the Client, he communicates in positive colors, but within a month he does not name a clear payment date. We can, of course, hide the site and hang it on the website Under Construction or Pay Off the Contractors.

We manage the domain, as it was bought, but apparently the Client does not understand this, and threaten - Like, pay, otherwise we don’t want to put it on Under Construction, because the Client is prospective. What do you advise?