Calling itself the Brigade of the Two Holy Mosques, a stark warning was published on an Islamist internet site on Wednesday.
The threat comes just days after Riyadh named 26 mostly Saudi suspects and posted financial rewards for information leading to their arrests.
"We are warning anyone who cooperates with the authorities or gives the tyrants information leading to the arrest of one of the mujahidin. He will be liquidated," said the statement.
It was countersigned by the "special operations" section of the brigade.
The group also threatened to "inflict a deterrent punishment on the person who denounced the martyr Ibrahim al-Rais."
Al-Rais, one of the 26 suspects, was killed on Monday in clashes with security forces in the capital.
This is the second public statement within a week by the previously unknown group, after it threatened to "cleanse" Saudi Arabia of anyone who has helped the United States.
"Whoever helps the infidels or spies on Muslims is an apostate," the group continued in its latest statement, using the term for people who renounce their religion.
"The Brigade of Death is committed to continuing the jihad (holy war) against the apostates," it said.
The Saudi authorities have offered rewards of up to $1.9 million for anyone who prevents an attack or gives information leading to the arrest of one of the suspects.
In recent months, the security services have stepped up policing, following attacks on residential compounds in May and November that killed a total of 52 people.
The group's name refers to the mosque of Mecca and the mosque of the prophet in Medina, both in Saudi Arabia, which are the two holiest sites of Islam.