NSA leaks: UK and US spying targets revealed
More details of people and institutions targeted by UK and US surveillance have been published by The Guardian, The New York Times and Der Spiegel.
The papers say that the list of around 1,000 targets includes a European Union commissioner, humanitarian organisations and an Israeli PM.
The secret documents were leaked by the former US security contractor, Edward Snowden, now a fugitive in Russia.
They suggest over 60 countries were targets of the NSA and Britain's GCHQ.
The reports are likely to spark more international concern about the surveillance operations carried out by the US and the UK.
News that the National Security Agency had monitored the phone of German Chancellor Angela Merkel triggered a diplomatic row between Berlin and Washington in October.
The New York Times reports that GCHQ monitored the communications of foreign leaders - including African heads of state and sometimes their family members - and directors of United Nations and other relief programmes.
The paper reports that the emails of Israeli officials were monitored, including one listed as "Israeli prime minister". The PM at the time, 2009, was Ehud Olmert.
The European Commission said in a statement that the claims, if true, "deserve our strongest condemnation".
"This is not the type of behaviour that we expect from strategic partners, let alone from our own member states."
Mr Almunia, a Spaniard, is responsible for approving mergers and investigating monopolies. He has clashed with the US firm Google.
The NSA denies carrying out espionage to benefit US businesses.
The Dutch Liberal MEP Sophia in 't Veld described the latest claims as "shocking".
"The UK spying on its fellow EU member states in order to get an economic advantage is simply unacceptable," she said.
GCHQ did not comment directly on the claims but said it operates "under one of the strongest systems of checks and balances and democratic accountability for secret intelligence anywhere in the world".
On Thursday a White House panel recommended significant curbs on the NSA's sweeping electronic surveillance programmes.
Edward Snowden left the US in late May, taking a large cache of top secret documents with him.
He faces espionage charges over his actions and has been granted temporary asylum in Russia.