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Here's the thing about the ICC's jurisdiction: It extends to crimes committed in countries which recognize that jurisdiction, even when the alleged criminals aren't from those countries.
Consider an American visiting, say, Paris, who's accused of a murder there. Just because he's an American, it doesn't follow that the French courts have no jurisdiction to have him arrested and tried -- whether the US regime "recognizes" that jurisdiction or not.
Joe Biden wants to have it both ways on that "very strong point."
His administration opposes ICC investigations into alleged Israeli crimes in Palestine because, as Secretary of State Antony Blinken points out, "Israel is not a party to the ICC and has not consented to the Court's jurisdiction." But the state of Palestine -- where the alleged crimes occurred -- is an ICC jurisdiction area, bringing Israelis who commit crimes there under its purview.
Nor does it seem likely that he'll reverse the Trump administration's denial of ICC jurisdiction over alleged US war crimes in ICC member states such as Afghanistan.
Interestingly, Ukraine isn't an ICC member state. It just selectively "accepts ICC jurisdiction" in certain matters. Read: Matters concerning alleged crimes by regimes with which it's at odds. Let a Ukrainian politician come under ICC scrutiny and such "acceptance" will likely pull a screeching 180-degree turn.
In practice, the ICC seems interested in investigating and prosecuting war crimes wherever it's allowed to. Which means: Wherever the US and EU regimes like it, or at least don't mind too much.
Vladimir Putin no doubt has a lot to answer for, but he's not alone.
As a US Senator and vice-president, Biden supported the US war in Afghanistan, and as president arguably approved war crimes there even as he oversaw the US exit from the conflict. Throwing himself -- not to mention several of his predecessors -- on the mercy of the court would make, in Biden's own words, a "very strong point."
If he's serious about making such points, he should ask the US Senate to ratify the Rome Statute, placing himself under the court's jurisdiction as well.