A report which criticises 14 European governments for complicity in CIA operations is expected to face a close vote in the European Parliament.
The CIA is believed to have flown at least 1,200 flights
The report says countries including the UK, Germany, Italy and Spain, turned a blind eye to CIA flights used to transport terror suspects.
Last year, the European Parliament set up a temporary committee of MEPs to investigate the allegations.
The claims were first published in the Washington Post in November 2005.
Delegations of MEPs travelled to countries including Romania, Poland, the UK, the United States and Germany to investigate claims of European involvement in so-called extraordinary renditions.
The report defines extraordinary renditions as instances where "an individual suspected of involvement in terrorism is illegally abducted, arrested and/or transferred into the custody of US officials and/or transported to another country for interrogation which, in the majority of cases involves incommunicado detention and torture".
The report says the CIA operated "at least" 1,245 flights in European airspace or stopped over at European airports. Some, but not all it says, were used for extraordinary renditions.
The committee heard evidence from government ministers, including the Spanish Foreign Minister Miguel Angel Moratinos, officials such as the EU foreign policy envoy, Javier Solana, and the EU counter-terrorism co-ordinator Gijs de Vries.
One of the most outspoken MEPs on the committee, British Liberal Democrat Baroness Sarah Ludford, says they also examined documents, including flight logs, "and some which, frankly, came to us in brown paper envelopes".
Baroness Ludford said: "We believe there has been either active collusion by several EU governments, or turning a blind eye."
The report is especially critical of Italy, Britain and Germany.
In the case of Britain, it "deplores" the manner in which the UK government co-operated with the temporary committee.
It condemns the extraordinary renditions of one British citizen and three British residents. Two of them, it says, were tortured; two are still held at the US detention facility in Guantanamo Bay.
It is also "outraged" by a legal opinion from a Foreign Office advisor, who said "receiving or possessing" information extracted under torture, in so far as there is no direct participation in torture, does not violate a UN convention.
The report says Italian intelligence officials played an active role in the extraordinary rendition of an Egyptian cleric, Abu Omar.
It also "regrets" that the abduction of Abu Omar "jeopardised (the public prosecutor's) investigation into the terrorist network to which Abu Omar was connected".
Germany is criticised for failing to accept a US offer to release a German resident, Murat Kurnaz, from Guantanamo Bay, even though "all investigations concluded, as early as the end of October 2002, that Murat Kurnaz posed no terrorist threat".
Some of these clauses may be watered down or rejected in the final vote in the parliamentary plenary. The report has been highly controversial.
For the leader of the British Conservative group, Timothy Kirkhope, it is enough to make him think again about the validity of some of the parliament's work.
He said: "What is the European Parliament doing, investigating in this way, when there has already been an investigation?
Mr Omar was allegedly kidnapped on a Milan street
"We do a lot of good things for European citizens, but this, I am afraid, has not shown us up in a very creditable light."
Last year, the human-rights body, the Council of Europe, carried out its own investigation, which concluded that European countries had helped the CIA to spin a "spider's web" of disappearances, secret detentions and illegal flights.
However, it failed to produce anything more than circumstantial evidence.
And Mr Kirkhope, like many of those opposed to the report, say the committee has been driven by an anti-American agenda.
For some MEPs, it has placed them in a difficult position.
The British Labour group in the parliament is now prepared to vote in favour of the report which criticises the Labour government in the UK but only after specific and personal criticisms of the Europe minister, Geoff Hoon, were dropped.
Labour MEP Claude Moraes said: "What we wanted, as Labour MEPs, was not to go into a situation where subjective, party political criticisms were made.
"We can definitely vote for a report which promotes human rights by asking proportionate, balanced questions of every country where allegations have been made, and that of course includes the UK."
Baroness Ludford, though, says the work of the European committee has spurred on other enquiries by national authorities.
In four countries - Germany, Italy, Portugal and Spain - prosecutors are now investigating suspected cases of extraordinary rendition.
She said: "It is about making sure we uphold the standards we proclaim.
"I am as dismayed as anyone at the declining reputation of the United States. That is of no benefit to anyone in Europe."
In its conclusions, the report says EU countries which persistently violated human rights should face diplomatic sanctions. That is unlikely to happen, as it would require unanimous assent from all 27 EU member states.
But it is a reminder of how seriously MEPs have taken the allegations, and the consequences those charges could bring.