"We warn the Saudi government and those who help it in its war against Islam ... that what is coming will be spectacular, so beware, tyrants of the Saudi family," said the statement posted on Saturday on a web site usually used by Islamic militant groups.
The authenticity of the statement by the group calling itself Basha'er (Good Tidings) could not be verified.
On Friday, Saudi police killed six insurgents in a three-hour clash which began after they surrounded a house to prevent what they said were planned attacks by the insurgents.
"The (Saudi royal government) killed our brothers ... and instead of allowing the light of jihad (holy struggle) to shine, this infidel government tries to put it out," the statement said.
It gave details about some of the six men, whose names were published earlier by the Saudi interior ministry.