ATLANTA — Some of the biggest names in national politics jumped into the fiercely contested runoffs for two Georgia Senate seats Friday, even as a second recount showed that Joe Biden had maintained his lead in the state and Republicans braced for a visit by President Donald Trump, who has railed against his loss there with baseless claims of fraud.

With Trump set to campaign for the two Republican incumbents, David Perdue and Kelly Loeffler, on Saturday, Vice President Mike Pence and former President Barack Obama held dueling events to underscore the vital stakes in the special elections: If both Republicans are defeated, control of the Senate will shift to Democrats just as Biden moves into the Oval Office.

Obama appeared virtually at a turn-out-the-vote event for Jon Ossoff, the Democrat facing Perdue, and the Rev. Raphael Warnock, Loeffler’s opponent, and spoke of his frustration in seeing his initiatives blocked by the Republican-controlled Senate when he was in office. “If the Senate is controlled by Republicans who are interested in obstruction and gridlock, rather than progress and helping people, they can block just about anything,” Obama said.

Pence — with Perdue and Loeffler by his side — received a COVID-19 briefing at the Atlanta headquarters of the Centers for Disease Control and Prevention and said later at a rally for the Republican candidates that “we’re going to save the Senate, and then we’re going to save America.”

A second recount of the presidential vote in Georgia has finished, according to the Secretary of State website, showing Biden ahead by about 12,000 votes with 100% of the counties reporting.

New campaign financial reports filed late Thursday showed a staggering influx of money into the state in the first days of runoffs that were expected to set spending records, with more than $300 million booked in television, radio and digital ads, according to data from AdImpact, an ad-tracking firm. Media buyers said the price of ads was soaring, especially for super PACs, to unseen heights.

The Senate races are playing out at a hyperpartisan moment in American politics that has led to a civil war among Georgia Republicans divided over whether to support Trump as he persists with false assertions that the election was stolen from him.