Can I use Database Engine Tuning Advisor for Azure? I am trying to use "Database Engine Tuning Advisor" for queries in Azure SQL.

According to https://docs.microsoft.com/en-us/sql/relational-databases/performance/start-and-use-the-database-engine-tuning-advisor it should work with Azure SQL.

However it gives me "Failed to open a new connection".


  ADDITIONAL INFORMATION: Database Engine Tuning Advisor does not
  support Microsoft Azure SQL Database. (DTAClient)


Is it correct? I found a thread  on MSDN forums(asked at December 2016)  
that confirmed that  Tuning Advisor worked with Azure in Microsoft® SQL Server® 2016 Service Pack 1 (SP1)

Is it still supported in Sql Server Management Studio v17.3 (Database Engine Tuning Advisor 14.0.1000.169), that I am using?
What should I do to enable it?

I've tried Azure Performance Insights, but it doesn't allow me to get suggestions of indexes for individual queries that I have to analyse.
No. The error message is correct - it does not support Azure SQL. There is no SQL 2016 for "Azure SQL", but there is SQL 2016 on an Azure VM, which is the same as any traditional SQL Server installation (more or less). 

That thread was confused, I assume, between SQL Server on an Azure VM and Azure SQL. 

Using the Azure Portal you should be able to check out index autotuning.