ArcGIS Pro cna't establish the connection with ArcGIS Online

[M__S__P__M_Siriwardane]

There is problem when trying to sign in to the ArcGIS Pro. It's blocked and cant sign in

[JayantaPoddar]

Could you check the network firewall (add the URL in trusted sites of Internet Explorer) or proxy settings?

See a similar issue here

Unable to establish connection to www.arcgis.com from ArcGIS Pro? - GIS StackExchange 

[fakhar_eddinahmed_abdalla]

There is problem when trying to sign in to the ArcGIS Pro. It's blocked and cant sign in

[FernandoVasquez]

How is the solution???

[MarkGoetz2]

Had same issue.   In Internet Explorer, under Advanced Settings,the Use TSL 1.2 was not checked.  Once checked, ArcGIS Pro opened without issue. 

[PhilipUhl]

Mark's solution is correct. Esri stopped allowing connections not using TLS 1.2 earlier this year. 

Open IE > Tools Menu (press Alt-T if you don't see the Tools menu) > Internet Options > Advanced > Check "Use TLS 1.2" checkbox > Apply

[Miami-DadePublisher]

Thanks, had a user with the same issue and this worked perfectly. 

[DanielEisenberg]

But why is ArcGIS Pro requiring IE and accessing IE's settings in the first place? Why would a desktop software solution need a browser  to connect to the web at all? IE is not my default browser and I never ever use it. Is there a way within ArcGIS Pro that I can set this to not depend on IE?

[DanielEisenberg]

I am asking these questions because I am getting warnings similar to the OP yet my IE was already set to use TLS 1.2, and *arcgis.com was already in my trusted site, and also because it seems like any web connections used should be set in the software's properties independent of any browser. 

I got the warning when I changed to OSM basemap - I am going to guess that it is the origin of this 3rd party service that is the crux of the immediate issue, but I don't see any documentation that will let me "trust" it.