Karzai (l) is a distant relative of Zahir Shah
Speaking after talks in Rome former King Zahir Shah, he said his new administration would fight against terrorism to "its absolute end".
An advanced force of 100 British troops is expected in Kabul on Saturday, when Mr Karzai will formally take power, the first of up to 5,000 troops under a UN mandate.
The UN Security Council is expected to vote on Thursday on a resolution which would formally establish the force.
US special forces in Afghanistan are continuing the hunt for Osama Bin Laden, but Pentagon officials admit they have no idea where he is.
Mr Karzai said he would have Osama Bin Laden arrested and put on trial, given the chance.
Unifying figure
The former king is seen by many Afghans as a unifying figure in the fractured country, and is expected to preside over a loya jirga, or grand council, which is to decide on Afghanistan's future.
Mr Karzai, a distant relative of the king, said the former monarch had given him much fatherly advice during Tuesday evening's meeting.
While in Rome, Mr Karzai also had a meeting with the Italian Prime Minister, Silvio Berlusconi, who promised millions of dollars in aid, and assistance in setting up a television station.
Mr Karzai is returning to Kabul by the weekend for the swearing-in of the new interim administration which he will head for six months, paving the way for a two-year transitional government.
In other developments
Sign of respect
The man picked to lead the new Afghanistan received the blessing and the personal Koran of the country's ex-king.
Mr Karzai belongs to the same clan as the ex-king, and his grandfather, Abdul Ahad Karzai, was president of the parliament in Kabul during part of the former king's reign.
"This is a copy of the Holy Koran, that His Majesty just presented to me as a guidance to go back to Afghanistan and be successful," he said.
"I am so very much touched... I shall kiss the Holy Koran as a sign of respect. I shall kiss His Majesty's hand as our king and father," he said.
"Before the changes in Afghanistan, I used to come here almost every month to work for the loya jirga," Mr Karzai said after arriving in Rome.
"I used to go and pay my respects to his majesty, the former king... I've come to do the same here this time."
Temporary figurehead
The future political role of the ageing former monarch has yet to be decided.
Because of his age and frailty, it is unlikely that he can be more than a temporary figurehead.
Correspondents say his presence in Afghanistan could be crucial, at a time when the political upheavals of recent years appear to be coming to an end.
Before meeting the former king, Mr Karzai warned rival anti-Taleban factions to submit to the control of a central defence ministry.
Many observers have expressed fear that, with the Taleban now overthrown, feuding warlords could again vie for control of the country.
"We have a ministry of defence and all forces in Afghanistan must eventually be under the ministry of defence," Mr Karzai told reporters.