Williams calls his rival a coward.
Williams insisted he would seize upon Klitschko's lack of a true fighting heart to bring the WBC world heavyweight title back to Britain.
The normally quietly-spoken 31-year-old from Brixton said: "Klitschko has a yellow streak in him.
"He does not like it when things get tough. His heart is definitely a weakness and it is up to me to expose it once again."
Klitschko has had to live with the tag of 'quitter' since retiring on his stool at the end of the ninth round of his WBO title defence against Chris Byrd in April 2000.
He had torn his rotator cuff in his left shoulder earlier in the bout and later underwent surgery and endured an eight-month lay-off.
But Williams pointed to his amazing British title battle with Mark Potter five months later by way of comparison.
Williams dislocated his right shoulder early but fought on bravely despite mounting calls from ringside for him to give up.
In the sixth round Williams let fly with a crashing left hand which sprawled Potter semi-conscious on the canvas and gained him one of the British sport's most remarkable wins.
Williams added: "I never thought I would knock out Potter with my right arm as bad as it was.
"I proved that when I was in a situation like that I did not feel pressure so I could perform at my best.
"But Klitschko only half-hurt his shoulder near the end against Byrd when he was way ahead on the scorecards.
"He just pulled out and said he would live to fight another day. Those are not the words of a true warrior."
Klitschko believes he more than proved a point when he was willing to fight on with his face a mask of blood against Lennox Lewis before the doctor ordered the contest stopped last year.
"People are entitled to their opinion but I fought hard against Byrd and I didn't want to stop but I had to stop," he said.
"If I had continued I could have damaged my shoulder even more seriously and I could have threatened my career. I am not super-human."