The alleged spiritual leader of the Jemaah Islamiya also warned the US to stop what he called the persecution of Muslims.
Bashir is set to be released on 30 April after serving his 18-month sentence for immigration violations, according to his lawyers.
But foreign governments, including Australia and the United States, claim he has no right to go free, and that his release could incite further violence.
Indonesian police are scouring interrogation transcripts from the US-held Jemaah Islamiya suspect known as Hanbali for evidence which may be used to implicate Bashir.
"I challenge the United States' officials to come here and question me. They are spreading lies. It is unfair," Bashir told reporters by phone from jail.
Bashir slammed Australia for its "insolence" in meddling with his release. "This is despicable. It is unethical for [Australia] to interfere with another country's judicial decisions."
"I challenge the United States' officials to come here and question me. They are spreading lies. It is unfair"
Abu Bakr Bashir,
leader, Jemaah Islamiya
He also warned Washington to stop what he called the persecution of Muslims. "If the United States continues to do so, there are many Muslim fighters that have sworn to destroy the enemies of Islam, including America and its allies."
However, he denied a report on Saturday in The Weekend Australian newspaper which quoted him as saying: "The Australian people will be hit" because of Canberra's alliance with the US.
The 65-year-old cleric was detained shortly after the October 2002 Bali bombings that killed 202 people, mostly foreign tourists. However, he was not charged over that attack, nor over a human bombing last year at the JW Marriott Hotel in Jakarta that killed 12 people.
According to media reports, Hanbali's interrogation notes link Bashir to bombings across Indonesia. Hanbali has been in US custody since being arrested in Thailand last August.
However, Indonesian officials said it was unlikely that the US transcripts could be used in court. They have said they want direct access to Hanbali or his return to Indonesia, which the US has not approved.
Earlier this year, the Indonesian Supreme Court cut Bashir's three-year sentence in half.