Citing high-ranking security sources, the Al-Seyassah daily said the 14 men fled to Iran on speedboats hours after Kuwait's supreme court sentenced them to lengthy jail terms for plotting attacks in the Sunni-ruled emirate.
Kuwait's interior ministry was not immediately available for comment.
The supreme court last month overturned an acquittal by the appeals court and sentenced 21 defendants to jail, including one for life, for forming a cell with ties to both Shiite Iran and Lebanon's Hezbollah movement and for planning attacks in Kuwait.
Around a third of Kuwait's native population of 1.35 million is Shiite.
Kuwait is leading mediation efforts in a regional crisis pitting Qatar against Saudi Arabia and its allies over accusations Doha is too close to Iran and funds Islamist groups.
Qatar has denied the allegations.
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