The 41-year-old Elliot, who is running left of Lamont, was looking to unseat the current Connecticut governor, who is seeking a third term.
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Elliot, a progressive Democrat, criticized Lamont as hesitant to raise taxes on the rich.
Lamont, 71, a wealthy former cable entrepreneur, has developed a reputation as a fiscal moderate, signing a major tax cut and paying down unfunded state pension liabilities.
He has also supported access to abortion through safe harbor laws and greater protections for immigrants.
Lamont will now face Republican Ryan Fazio in the general election in November.
No Connecticut governor has served three consecutive terms in modern times.
Just one governor in Connecticut has won a third term in the last 200 years, Gov. John Rowland, who resigned in 2004 before completing his third term.
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