The letter also notably praises a top Iraqi Shia leader, Ayat Allah Ali al-Sistani.
"Sayyid al-Sistani has our appreciation," it said, using the title for a descendant of the prophet Muhammad.
Al-Sistani is viewed by US officials as a crucial force for Shia cooperation in post-war Iraq.
But the cleric has expressed unhappiness at the US occupation and demanded the US allow Iraqis to rule themselves.
To date, Iraq’s Shia have remained relatively passive during the US-led occupation. However, in recent weeks, tensions have grown, particularly in the British controlled Shia-majority city of Basra.
The handwritten note was also the former Iraqi president’s condemning response to a journalist's questions about Ibrahim al-Jafari, the first president of Iraq's 25-member interim Governing Council.
Al-Jafari said that the Transitional Governing Council would set up 23 ministries to run Iraq but refused to name ministers until next week.
Proposals for new ministries include one for human rights, migration, women’s affairs and also for the reconstruction of South Iraq. But the former president urged Iraqis to end cooperation with all occupation forces.
At the beginning of August, Aljazeera aired another message from Hussain to the Iraqi people. It was the sixth audiotape attributed to him and broadcast by Arab satellite channels in less than a month.