In event log there was error with Event ID 1026, which stated that "The process was terminated due to an unhandled exception", the event source was .NET Runtime, and Framework version was v4.0.30319.
I checked the .NET version and it was 4.6, which is suported with SCVMM 2016.
The issue was only with console on SCVMM server not on remote consoles.
It turned out that I had installed there are two binaries of SCVMM 2016 update rollup that need to be installed on SCVMM server:
After installing also the admin console update (not just the VMM management server update), the issue was gone.