Journalist Walter Barasa has 14 days to appeal after which Kenya's Internal Security Ministry can arrest and extradict him to The Hague-based court.
Barasa did not demonstrate how his constitutional rights will be violated and that he is likely to suffer oppression and discrimination if arrested, said Judge Richard Mwongo when he declined to stop the arrest.
ICC Judge Cuno Tarfusser had issued a warrant for Barasa, 41, in October on suspicion of attempting to bribe a potential witness.
Bensouda said she hopes Barasa's arrest warrant will serve as "a warning to others who may be involved in obstructing the course of justice through intimidating, harassing, bribing or attempting to bribe ICC witnesses ... My office will continue to do everything it can to ensure that witnesses are able to present their evidence before the court without fear." If convicted, Barasa could face a prison sentence of up to five years.
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Ruto's trial continued this week but the case against Kenyatta may collapse because witnesses are withdrawing. Kenyatta's trial was to start in November but was postponed to February after the prosecution and defense teams said they needed more time to prepare.
The ICC prosecutor in December requested court for an additional three month adjournment after one witness withdrew and another admitted giving false evidence. At the time, ICC Prosecutor Fatou Bensouda said she needed time to reconsider her case.