Footage filmed by Reuters in Moscow showed law enforcement bundling people to the ground in the snow, close to a spot where mourners left flowers and messages supporting the dead opposition leader.
Some also chanted "Putin to the Hague", referring to the international criminal court investigating possible war crimes committed in Ukraine.
"Let us be clear, Russia is responsible," US VP Harris said, adding that it would be "a further sign of Putin's brutality" of the death is confirmed.
Goldschmidt, also President of the Conference of European Rabbis, also expressed his condolences to Navalny’s wife Yulia Navalnaya, and his children.
In a statement published on its website, the Federal Penitentiary Service said that Navalny "felt unwell" after a walk on Friday, and "almost immediately lost consciousness."
In a message on X facilitated by his allies, Navalny described a surreal morning routine.
Navalny, who has been sentenced to stay in jail until he is 74, has repeatedly warned that Putin's Russia is a state run by "thieves and criminals" and that one day there will be a revolt.
Navalny was tracked down to the IK-3 penal colony in Kharp in the Yamal-Nenets region, about 1,900 km (1200 miles) north east of Moscow, spokeswoman Kira Yarmysh said.
Kira Yarmysh said staff at the IK-6 facility in Melekhovo, 235 km (145 miles) east of Moscow, had told his lawyer waiting outside that the opposition leader was no longer among its inmates.
The Navalny family intends to take the case as far as the Constitutional Court, the politician said on Monday in a post on his official Instagram page, which is run by his lawyers and allies.