Gordon Brown has urged people to wait until the "full facts" of the police cash-for-honours inquiry are known.
The chancellor urged people to wait for the full facts
The chancellor said it would be inappropriate to comment on Lord Levy's arrest while the inquiry continued.
But asked if there had been some kind of "cover-up", he told the BBC: "I believe when people see the full facts then they will be satisfied."
No 10 says there is "unfairness" in them not being able to respond to press commentary while the inquiry continues.
Police are investigating whether money was donated to political parties in exchange for peerages - all those involved deny any wrongdoing.
Lord Levy, who has denied any wrongdoing, was first arrested last July, in connection with alleged honours offences.
He was re-arrested when he answered bail on Tuesday, this time on suspicion of conspiracy to pervert the course of justice, but was not charged and later freed on bail.
Downing Street has denied allegations it had a hidden e-mail system from which messages were deleted after the cash-for-honours inquiry began.
But the BBC's political editor Nick Robinson said the police clearly believed they were not being given all the information they needed - even after searching government computers - which could explain Lord Levy's latest arrest.
Liberal Democrat chief of staff Edward Davey said the "sorry affair" had the "whiff of Watergate about it".
And at prime minister's questions on Wednesday, SNP leader Alex Salmond asked Mr Blair whether, rather than his association with President Bush, an association with President Nixon might be more appropriate.
"Is there a cover-up in Downing Street?," he asked.
The prime minister's official spokesman has refused to comment on the arrest but said Downing Street had co-operated fully with police at all times.
He added that Downing Street felt uncomfortable that it could not answer some of the allegations being made during the course of the police investigation.
April 2006 - Des Smith
July 2006 - Lord Levy
Sept 2006 - Sir Christopher Evans
Jan 2007 - Ruth Turner
Jan 2007 - Lord Levy
Asked at prime minister's questions why he was refusing to comment, Mr Blair replied: "As you know, for perfectly obvious reasons, there's nothing I can say on this subject."
Downing Street said on Wednesday that Lord Levy was still the prime minister's Middle East envoy and continued to play a valuable role.
Chancellor Gordon Brown was asked about the arrest in a BBC Scotland interview on Wednesday.
He said: "I don't think it's appropriate for me to comment on a police investigation, let the investigation take its course and let it be concluded and then people will see the results of it."
Asked whether there had been some kind of cover up he said: "I think the police investigation has got to be completed then people will see the full facts and I believe when people see the full facts then they will be satisfied."
Another Blair aide, Ruth Turner, was arrested then bailed earlier this month.
The inquiry began after it emerged that a number of large secret loans had been made to the Labour Party before the 2005 general election, and that some of those lenders had subsequently been nominated for peerages.
The investigation has since widened to cover the other main parties, with Mr Blair and former Conservative leader Michael Howard among those questioned.
No-one has been charged and all involved deny any wrongdoing.