His former press secretary was arrested and faces questioning over his role in the scandal as former editor of the tabloid. Coulson has denied any knowledge of phone hacking while he was NoW editor.
The prime minister said: "I gave someone who screwed up a second chance. I judge people on the work they do for me ... the buck stops here."
He said "people will judge" how serious was his hiring of Coulson in relation to his judgment.
A separate investigation into phone hacking across the media will be carried out by a panel of experts he told a press conference.
He said it was no good "pointing fingers at individuals" and that a wider look into the way the media operates is needed.
"This is a wake up call. Things have got to change."
However, he added: "It's vital to have a free press."
He said News International chief executive Rebekah Brooks had offered to quit and that he would have accepted her resignation.