Based on the later discussion in the press, it seems that:
Turner himself didn't actually make that claim; he only said something more vague about a “serious national security threat”.
While the initial press speculation (cued by some anon "intel officials") seems to have centered on the nuke hypothesis, nobody from the administration, when queried publicly, would confirm that either. Only
White House spokesperson John Kirby confirmed that the threat in question is “related to an anti-satellite weapon that Russia is developing.”
- Later press speculation includes discussion whether it's a nuclear-powered high-energy electronic warfare weapon, such as what "Ekipazh" might be able to carry/power.
Nearly the same stuff was also said in a more high-profile source (The Economist).