Federal prosecutors in Brooklyn have been investigating whether several Ukrainian officials helped orchestrate a wide-ranging plan to meddle in the 2020 presidential campaign, including using Rudolph W. Giuliani to spread their misleading claims about President Biden and tilt the election in Donald J. Trump’s favor, according to people with knowledge of the matter.

The criminal investigation, which began during the final months of the Trump administration and has not been previously reported, underscores the federal government’s increasingly aggressive approach toward rooting out foreign interference in American electoral politics. Much of that effort is focused on Russian intelligence, which has suspected ties to at least one of the Ukrainians now under investigation.

The investigation is unfolding separately from a long-running federal inquiry in Manhattan that is aimed at Mr. Giuliani. While the two investigations have a similar cast of characters and overlap in some ways, Mr. Giuliani is not a subject of the Brooklyn investigation, the people said.