In some regions of the world, it is apparently not possible to access the purl.org website that hosts the redirect to the default global bundle file. Tectonic does not currently support HTTP proxies (relevant issue), but if you can skip past the purl.org redirect then things can work.
You can do this by creating the Tectonic configuration file, a process that isn’t currently documented elsewhere. (Sorry.) The configuration file is in TOML format. On Linux, Tectonic looks for a file named ~/.config/Tectonic/config.toml. On macOS/OS X, it is named ~/Library/Application Support/Tectonic/config.toml. You will need to create this file even if you’ve run Tectonic before, and you may have to create the directories that contain it.
As of this writing, the contents of this file should then be:
[[default_bundles]]
url = "https://dl.bintray.com/pkgw/tectonic/tl2016extras/2016.0r4/tlextras-2016.0r4.tar"
If you can access dl.bintray.com, Tectonic should then work for you, even if you can’t access purl.org.