Debunking the fact-checkers. DoD does fund outside the US - noted in this document from 2015. Selected excerpts - quite the read.
https://sgp.fas.org/crs/nuke/R43143.pdf
The Evolution of Cooperative Threat Reduction: Issues for Congress
Updated November 23, 2015
Nuclear Smuggling
Bioweapons
The CTR program has built a secure Central Reference Laboratories (CRL) for pathogen collections in Ukraine and Kazakhstan, and is constructing a CRL in Azerbaijan. Currently, the CTR program has completed upgrades at39 “Secured Labs” in Armenia, Georgia, Kazakhstan, and Ukraine. DOD continues to support upgrades and training at these facilities.89
Page 47: The ISTC headquarters have moved to Nazarbayev University inAlmaty, Kazakhstan. The United States provides support through the ISTC to the Biological Weapons Redirection Program