Publish WebAPI and MVC projects to same Azure Web Site?

Go to Azure portal and create an AzureWebsite -

Then setup an additional application in the settings as follows -

Now create two projects in the Visual studio solution -> 1) MVC and 2) WebApi

Download publishsettings file of above created azure website. Import the publishsettings file to the Visual studio MVC project publish as shown below -

And for WebApi project, import the same publish settings, but create a new path as website/webapi.

Publish both the projects.

Now navigate to http://{yoursite}.azurewebsites.net for the MVC site. And navigate to http://{yoursite}.azurewebsites.net/webapi/api for your WebApi.