Hello again, Kenji,
"Hold accountable" is an idiom, and here (in both cases) it means to consider someone responsible for something.
For example, "Mr. Pence vowed that the United States would ”hold Russia accountable, even as we search
to make a determined decision..." means that, if Russia's actions in Ukraine lead to more fighting, the US will consider Russia responsible for the conflict.
And when the article states "He said the United States would hold Russia to its commitments to reach a permanent cease-fire," it means that, because Russia made a commitment to reach a permanent cease-fire, the US considers Russia responsible to uphold the commitment it made (i.e. the US expects the Russians to honor their promises).
Hope that helps.