In a televised address read by Information Minister Mohamed Said Sahaf, the Iraqi leader said both Iraq and Kuwait had been victims of the Gulf War in 1991.
But he accused the leadership of Kuwait of conspiring "hand in hand" with those who were preparing to attack Iraq, and urged Kuwaitis to join the fight against this.
Saddam Hussein also apologised to the Kuwaitis for what he termed acts that had caused anger in the past, saying he wanted to set the record straight about Iraq's invasion of Kuwait in 1990.
"We apologise to God for any deed that angered him in the past, which we might not have known of and is blamed on us, and on this basis we also apologise to you."
The Kuwaiti Information Minister, Sheikh Ahmad al-Fahd al-Sabah denounced the message as an attempt to create rift between Kuwait's people and its leaders.
"The speech contained incitement and encouragement of terrorists acts which the whole world has rejected and condemned," Sheikh Ahmad told the Kuwaiti News Agency.
The BBC's David Bamford says President Saddam my have resigned himself to the belief that there will be war and this is a final appeal to Kuwaitis and the Arab world at large to resist.
Jihad calls
President Saddam said he was only trying to do for the Kuwaitis what he was doing for his own people.
"Brother, what we wish for you is the same as we endeavour to do for your brothers in Iraq; namely, for you to live free without foreigners controlling your destiny, will, decisions, wealth, present and future.
"And for you to work as free people and believers in a way that would serve your people and nation."
Referring to the presence of the US troops, he said Kuwait was under "direct foreign military occupation" and called on Kuwaitis to join efforts to expel them.
"Why will not the faithful, the devoted and the holy warriors in Kuwait meet with their counterparts in Iraq under the blanket of their creator, instead of under the blanket of London or Washington and the Zionist entity, to discuss their matters on top of which is the jihad against the occupation of infidel armies."
He went on to praise "devout youth who carry arms against the occupier" - in an apparent reference to militants who recently attacked US troops in Kuwait.
The Iraqi president said such a holy war would enable them to "cleanse the nation from shame" and relieve it of the "harm done to the people of Kuwait and Iraq".