The pair made the announcement shortly after performing at the Roundhouse in north London late on Tuesday, but they added that they hoped to record together soon.
"We sincerely apologize for the canceling of all of our tour dates," said the band, which comprises Joy Williams and John Paul White.
"It is something we deeply regret. However, due to internal discord and irreconcilable differences of ambition we are unable to continue as a touring entity at this time ... Our sincere hope is to have new music for you in 2013."
The band said it would "do its best" to reimburse fans who had made travel reservations to see them.
The Civil Wars released their debut studio album "Barton Hollow" last year and went on to scoop two Grammy Awards - the highest prize in music - for best folk album and best country duo/group performance.
(Reporting by Mike Collett-White)
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