MSPs have called on the Scottish Executive to detail any communications with the UK Foreign Office over US rendition flights landing in Scotland.
A protest against the flights was recently held at Edinburgh airport
However, they rejected a demand from the Scottish Socialist Party for a public inquiry into the controversy.
The US consul general in Scotland has denied that Scottish airports have been used as stopovers for flights carrying terror suspects for alleged torture.
Cecile Shea also said there was no evidence to back up the claims.
'Barbaric and illegal'
The US Government has confirmed that a number of rendition flights have taken place across the world but has dismissed allegations of prisoner abuse.
The SSP led the Holyrood debate on the flights, demanding that the lord advocate instruct the police to investigate.
Socialist MSP Frances Curran said MSPs should demand to know the truth about Scotland's role in "this barbaric and illegal practice of secret kidnappings".
Liberal Democrat Jim Wallace said the UK Government should immediately hold an independent inquiry.
But the former deputy first minister advised caution that the political independence of the police and prosecuting law officers was not compromised while trying to address the issue of torture.
Scottish National Party MSP Sandra White said that if the EU, Spain, Sweden, Iceland and Manchester Police were to launch an inquiry, the same should happen in Scotland.
She said: "We wish an inquiry, the country wishes an inquiry, the Scottish people want to know the truth. We demand to know the truth."
Green MSP Chris Ballance claimed much evidence into rendition flights landing in Scotland had been gathered.
He said the Swedish parliamentary ombudsman had listed dates of when a CIA rendition plane had refuelled at Prestwick Airport, which were accompanied by photographic evidence.
Mr Ballance asked: "What more evidence do our police require before acting?"
Tory North East MSP Alex Johnstone said Britain should be concerned if it appeared that its allies in the United States were now flouting international agreements.
Earlier, Ms Shea told BBC Radio's Good Morning Scotland programme: "We do not extradite people through extraordinary measures or through traditional measures so that they will be tortured, and do not extradite them if we believe they will be tortured.
"Washington has asked us throughout Great Britain to make this point very, very clear and I really don't know how much more clearly we can make it. We just are not doing this."
Until now the Scottish Executive and Scottish police have refused to open an investigation, saying that no evidence has been produced to justify the measure.