The mysterious incident took place on February 22 just five days before the start of a nuclear summit between North Korea and the United States attended, among others, by Pyongyang's former ambassador to Spain Kim Hyok Chol.
According to investigators quoted by El Pais, they were specifically looking for information linked to Kim.
"At least two of the 10 assailants... have been identified and have ties with US secret services," the paper said, citing sources from the police and Spain's intelligence agency, the National Intelligence Centre (CNI).
It specifically identified the CIA.
Contacted by AFP, the CNI refused to comment.
According to El Pais, Spain asked for clarification from the CIA but the US spy agency denied any involvement.
Spanish authorities however said the response was "not very convincing".
The report said the CIA acted "in probable cooperation" with South Korean intelligence services.
The break-in has been surrounded by mystery.
According to El Pais, which has quoted investigators as saying this could be "political espionage", the 10 men entered with fake handguns, tying up and gagging the staff.
They reportedly escaped with documents, computers and telephones in two embassy cars with diplomatic number plates which they later abandoned.
Investigators have discarded the theory of a petty crime as the break-in was well organised and similar to a military commando operation that knew what it was looking for.
After analysing CCTV footage and questioning witnesses, they identified two of the assailants as having links with the CIA, El Pais said.
Since 2017, when Kim Hyok Chol was expelled from Spain as "persona non grata" after nuclear tests and missile firings by Pyongyang, the secretive state has had diplomatic representation in Madrid but no ambassador.
Kim is one of North Korean leader Kim Jong-un's most trusted officials.
The talks failed to reach a nuclear accord.
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