WASHINGTON — Republicans are wielding the power of their Senate majority to intensify an election-year investigation of Hunter Biden’s work for a Ukrainian energy firm, putting new scrutiny on the son of Joseph R. Biden Jr. as the former vice president re-emerges as President Trump’s chief rival for the presidency.

In elevating questions about the younger Mr. Biden’s work in Ukraine, Senate Republicans are effectively picking up where the president left off last year when he pressed the country’s leaders to investigate the Bidens, an effort that led to his impeachment in the House on charges that he abused his power by seeking foreign help in the 2020 election. It is part of a broader attempt by his allies on Capitol Hill to breathe fresh life into politically charged inquiries into issues that have preoccupied Mr. Trump.

Senator Ron Johnson, Republican of Wisconsin and the chairman of the Homeland Security Committee, plans to hold a vote next week despite Democratic objections to issue a rare Senate subpoena to Andrii Telizhenko, a former Ukrainian official who worked for Burisma, the energy firm. Mr. Johnson told reporters on Wednesday that he would release an interim report this spring summarizing what Republicans had learned from months of quiet queries.

For now, Republicans insist Burisma is a matter of longstanding interest unrelated to Mr. Biden’s presidential candidacy, and no evidence has emerged to suggest that either Biden acted improperly. But Mr. Johnson acknowledged that his investigation could affect the election and said that was as it should be.