Update: Since Publish Web does not apply to folder-based web site projects, this answer assumes you are asking about a Web Application project.
You can't do this from inside the VS IDE. However, you can edit your project file in Notepad or your favorite XML editor and add a new target at the end of the file called
You might want to read a bit more on MSBuild if you are not sure what you can do in this target.
You can find more details on extending the build process in VS at MSDN - HowTo: Extend the Visual Studio Build Process.