Ossoff has been counting on uniting Democrats in Georgia's special election.
Democrats heavily pushed Ossoff before Tuesday's vote, casting the race as a referendum against President Trump in hopes of turning the reliably red district blue.
Georgia's Sixth Congressional District has historically consistently elected Republican candidates.
Had Mr Ossoff managed to get more than 50 per cent of the total, he would have won outright.
Ossoff and Handel will face off in a June 20 runoff to succeed current U.S. Health and Human Services Secretary Tom Price in a district that has been in Republican hands since 1979 and remains in the national political spotlight.
Still, opinion polls show Ossoff leading his many rivals. We all have to rise above it, that it is about the district that has a long legacy of Republican leadership, from my good friend current HHS Secretary Tom Price, to Senator Isakson and former Speaker Newt Gingrich.
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Trump was heavily invested in the race and in a tweet claimed victory, although Ossoff could still win in the runoff.
But Trump's sharp-elbowed cultural worldview and provocative rhetoric helped Hillary Clinton make serious inroads in a place populated by wealthy, well-educated white voters, many of whom defected en masse from the GOP leader's ticket a year ago. Trump won the district by only about one point over Hillary Clinton.
The victor in Georgia will succeed Republican Tom Price, who resigned to join Trump's administration as health secretary.
The Democratic candidate, a former congressional aide and the owner of a investigative film company, is only 30 years old.
Ossoff raised a stunning $8.3 million in the first quarter, forcing Republicans to spend heavily against him.
Republican Senator Lindsey Graham of SC said the race showed how the South was changing. Democrats are also looking to build momentum heading into next year's midterm elections. "Say NO", Trump tweeted. "That way we can cut spending and get our economy back on track and keep America safe".
While some polling suggests Ossoff still stands a chance at winning the seat, the task in front of him now is a much steeper climb than what he has faced up to this point. Or will Democrats regard it as a disappointment given the ideal storm of factors that seemed to be lining up in Ossoff's favor for Tuesday's vote?
The move by Ryan - one of the most powerful Republicans in government - to insert himself into a special election in a GOP district speaks volumes about how anxious Republicans are about this race.