The attacks in Iraq included a bombing that killed more than 100 people last year, one of their lawyers in Stockholm said on Tuesday.
The two men, aged 25 and 29 respectively, will go on trial on Thursday on charges that they sent about $148,000 to the Ansar al-Islam and Ansar al-Sunna groups and to Iraq's most wanted man Abu Musab al-Zarqawi, said the younger man's lawyer Ola Salomonsson.
Prosecutor Agneta Hilding Qvarnstroem has charged that the money was, among other things, used for a bombing in the northern Iraqi city of Arbil on 1 February 2004, that left more than 100 people dead.
"My client has said that he has received money that he sent on, but the money was not for bombings. It was supposed to go to people who needed help, for social causes," Salomonsson said.
"The amounts the prosecutor has given are not right either. My client says he does not know how much money there was, but that it was not that much," he added.
According to his lawyer, the 25-year-old had been working within the hawala system, an ancient underground banking system used mainly in South Asia and the Middle East to transfer money internationally while circumventing legal and financial barriers.
The two defendants were arrested with two other men in Sweden last April suspected of direct participation in attacks in Iraq.
"... there are a number of uncertainties in the charges brought by the prosecutor. She is the one who has the burden of proof"
Due to lack of evidence prosecutors were forced to drop the charges against the other two men at the end of last summer and to reduce the charges against the two defendants.
Last December, the Swedish government said it planned to extradite one of the men still in custody.
"We have decided to extradite an Iraqi man who we feel could participate in terrorist activities. We cannot do so immediately since there is a risk that he could be executed" in Iraq, Justice Minister Thomas Bodstroem said at the time.
"If [my client] is found guilty of this crime, he will almost certainly be expelled," Salomonsson acknowledged, but added that "there are a number of uncertainties in the charges brought by the prosecutor. She is the one who has the burden of proof."
The trial is expected to last until the end of April, the lawyer said.