Yasin Majeed, al-Maliki's media adviser, told the Reuters news agency that "al-Zaidi said in his letter that his big ugly act cannot be excused".
According to Majeed, al-Zaidi asked the prime minister to recall the kindness al-Maliki showed him during a 2005 interview when he invited the journalist to his home.
"I appeal to your fatherly feelings to forgive me," al-Zaidi was quoted as saying by Majeed.
However, Dhargham al-Zaidi, the journalist's brother, questioned whether the statement was genuine.
And an Iraqi judge said on Friday that al-Zaidi was beaten and had bruises on his face and around his eyes.
Dhia al-Kinani, the magistrate investigating the shoe-throwing incident, said the court has opened an investigation into the alleged beating.
Instant fame
Al-Zaidi shot to instant fame when he called Bush a "dog" in Arabic at a joint news conference with al-Maliki in Baghdad on Sunday and threw both his shoes at Bush in a gesture that is a deep insult in Arab culture.
His whereabouts remained unknown four days after he became a hero to those who blame the American president for the tens of thousands of Iraqi deaths that followed the 2003 US-led invasion of Iraq.
His family says he suffered a broken arm and other severe injuries after he was tackled by Iraqi security officers and US secret service agents and dragged away struggling and screaming.
His family says he is in a hospital in Baghdad's heavily guarded Green Zone.
On Tuesday, al-Zaidi was brought before an investigatory judge and admitted to committing "aggression against a president", a crime that carries a 15-year prison sentence, judicial officials said.
He could face trial soon on the charge.
Vocal support
Al-Zaidi has received vocal support from fellow Iraqis who have demanded his release, and similar support was shown from Bethlehem to Montreal on Thursday.
In Bethlehem's Manger Square, in the West Bank, several dozen Palestinian journalists took off their shoes to protest against al-Zaidi's detention and carried signs saying "Bush deserved it".
And in the Canadian city of Montreal, Block the Empire, an anti-war protest group that regularly criticises Bush's foreign policy, invited Canadians to hurl their footwear at the US consulate in the city on Saturday in solidarity with al-Zaidi.