The US does not recognize such an argument. If that is the argument being made, then no wonder the US issued sanctions; it would perceive such a precedent as a threat to its sovereignty.
Not quite: The US helped invent that argument, and has used it extensively to pursue its foreign policy goals since World War II.
What the US has argued historically is that American people and institutions are not subject to it because the US has a functioning civilian and military justice system, and so prosecution for such crimes can be handled within it, even by foreign nations and NGOs.
Obviously that’s a load of bullshit, especially (but not only) these days, but “sovereignty for me but not for thee” has long been the rule and with its weakening international position the US may come to find that to be less achievable in the future.
When has the US used the argument that a judicial system has universal jurisdiction? In the US, foreign policy is the domain of the executive, to the point where court cases involving foreign sovereigns are usually dismissed.
Compared to how much of a mess most of the world's powers are on matters on sovereignty, the US is actually one of the more conservative ones here (e.g., see OFCOM in the UK).
Let me restate: The US position is that the US justice system “works” and thus *US persons and institutions* must be pursued *within the US system* even by foreign entities.
In other words, the US position is not that if (say) North Korea commits a crime against humanity they must be pursued in US courts; the US is fine with the ICC in that case. The US position is that if the US commits a crime against humanity that must be pursued in US courts, not the ICC.
It’s an obvious (and bullshit) double standard, but it’s also not a denial of the legitimacy of universal jurisdiction. It’s just the US, as usual, trying to have its cake and eat it too.
Why is that a double standard? The US position is that recognized nations have sovereignty, and are the supreme law within their jurisdiction. If there is no recognized legitimate sovereign power, then the US is fine with an international body substituting.
That this standard is complicated, and different from those that argue that international law should be the supreme law, doesn't make it a double standard. It's also not what is meant by universal jurisdiction, as it does not depend on overriding sovereignty.
Edit: Seeing your other comment, it's also worth noting this was a large reason why the US didn't sign the Rome statute, since as you note, the US isn't inherently opposed to the idea of international courts, only the supremacy of their jurisdiction.
The US doesn’t believe universal jurisdiction applies to it or its vassal states and proxies, which includes Israel.
On the other hand, the US didn’t try to prevent Slobodan Milošević from being tried at The Hague for war crimes and genocide, as Serbia wasn’t a vassal state or proxy.
They don't want the precedent established. Same reason why uninvolved parties in US courts submit "amicus briefs" - the precedent from a case may affect them down the line.