"It is too late to now regret the big and ugly act that I perpetrated," Muntadhar al-Zeidi wrote, according to Majid.
Majid told the AP that al-Zeidi went on in the letter to recall an interview he conducted with the prime minister in 2005 when al-Maliki invited him into his home, saying: "Come in, it is your home too."
"So I ask for your pardon," al-Zeidi wrote, Majid said.
Iraq's president, Jalal Talabani, can issue a pardon if recommended by the prime minister, except for certain offenses including international crimes, according to Iraq's constitution.
Iraqi officials had said al-Zeidi would probably be charged with insulting a foreign leader, which potentially carries a two-year sentence.
Thousands took to the streets in Iraq to protest al-Zeidi's arrest, and his actions were heralded across the Arab world as news stations repeatedly showed footage of the shoe-throwing incident.
Iraq's parliament erupted into chaos Wednesday when lawmakers argued over the jailing of al-Zeidi and the hot-tempered parliament speaker, Mahmoud al-Mashhadani, said he was resigning.
It is unclear if al-Mashhadani, who has a history of erratic behavior and threatening to step down from his role as speaker, intended to actually leave his post. But he appeared at the legislature on Thursday.
The Iraqi prime minister was standing next to Bush at the Sunday news conference where the journalist, a correspondent for an Iraqi-owned television station based in Cairo, Egypt, threw his shoes.
The journalist also shouted at Bush in Arabic, "This is your farewell kiss, you dog! This is from the widows, the orphans and those who were killed in Iraq."
Al-Zeidi was tackled to the ground by Iraqi and U.S. security after throwing his shoes at Bush, who deftly ducked.
Al-Zeidi remained in custody Thursday night.
An investigative judge visited al-Zeidi in his jail cell earlier this week and the family was told to return to court next week, according to the journalist's brother, Dhargham al-Zeidi.
Dhargham al-Zeidi claims his brother was harshly beaten after being taken into custody.
However, Iraqi officials and another brother have denied that the journalist suffered severe injuries.