No one has yet claimed responsibility for the attacks but observers quickly noted that the methods used resembled those of the extremist organization.
Seven people are believed to have been killed and two wounded in the Medina attacks, at a Shiite mosque in Qatif and in western Jeddah, the economic capital, not far from the US consulate.
Suicide bomber killed, two police wounded in blast outside US consulate in Jeddah
"Those three attacks were, I think, the work of ISIL," Brennan said at an event at a Washington think tank, using the US government's preferred abbreviation for the Islamic State group.
"ISIL presents a very, very serious threat not just to Europe and the United States... but inside of Saudi Arabia," he told an audience at the Brookings Institution.
Several days after the attacks, the Saudi interior ministry announced the arrests of 19 suspects, including 12 Pakistanis.
Regional heavyweight Saudi Arabia is part of the US-led international coalition battling the IS group in Iraq and Syria.
Four security officials killed in suicide blast outside Masjid Nabawi
Since March 2015, the country has also led a coalition fighting Shiite rebels in Yemen.
In the past year, Saudi authorities have stepped up the arrests of radical extremist and in 2015 announced that they had dismantled an IS-linked group, detaining hundreds of suspects, mainly Saudis.
Saudi Arabia's top cleric, Sheikh Abdulaziz al-Sheikh, has declared the IS group to be an "enemy of Islam."
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