* NSA bugged offices, spied on internal networks -magazine
* U.S. agency "accessed documents, read emails" (Adds U.S. spokesman had no comment, paragraph 5)
BERLIN, June 29 (Reuters) - The United States has bugged European Union offices and gained access to EU internal computer networks, according to secret documents cited in a German magazine on Saturday, the latest in a series of exposures of alleged U.S. spy programmes.
Der Spiegel quoted from a September 2010 "top secret" U.S. National Security Agency (NSA) document that it said fugitive former NSA contractor Edward Snowden had taken with him, and the weekly's journalists had seen in part.
The document outlines how the NSA bugged offices and spied on EU internal computer networks in Washington and at the United Nations, not only listening to conversations and phone calls but also gaining access to documents and emails.
The document explicitly called the EU a "target".
A spokesman for the Office of the U.S. Director of National Intelligence had no comment on the Der Spiegel story.
Martin Schulz, the president of the European Parliament, said that if the report was correct, it would have a "severe impact" on relations between the EU and the United States.
"On behalf of the European Parliament, I demand full clarification and require further information speedily from the U.S. authorities with regard to these allegations," he said in an emailed statement.
Luxembourg Foreign Minister Jean Asselborn told Der Spiegel: "If these reports are true, it's disgusting.
"The United States would be better off monitoring its secret services rather than its allies. We must get a guarantee from the very highest level now that this stops immediately."
Snowden's disclosures in foreign media about U.S. surveillance programmes have ignited a political furore in the United States and abroad over the balance between privacy rights and national security.
According to Der Spiegel, the NSA also targeted telecommunications at the Justus Lipsius building in Brussels, home to the European Council, the collective of EU national governments.
Without citing sources, the magazine reported that more than five years ago security officers at the EU had noticed several missed calls and traced them to NSA offices within the NATO compound in Brussels.
Each EU member state has rooms in Justus Lipsius with phone and internet connections, which ministers can use.
Snowden, a U.S. citizen, fled the United States to Hong Kong in May, a few weeks before the publication in the Guardian and the Washington Post of details he provided about secret U.S. government surveillance of internet and phone traffic.
Snowden, 30, has been holed up in a Moscow airport transit area since last weekend. The leftist government of Ecuador is reviewing his request for asylum. (Reporting by Annika Breidthardt and Ben Deighton in Brussels; Additional reporting by Tabassum Zakaria in Washington; Editing by Kevin Liffey and Eric Beech)