Per Steffensen told Danish sports website www.sporten.dk that Agger must rest for four weeks after sustaining the injury during Liverpool's 4-0 defeat at Tottenham Hotspur on Sunday.
"Daniel has fractured the top two ribs. It's so annoying. He now has to lie still for four weeks before resuming training. He's sad, and it's annoying because now we'll be hearing all these stories about how he's injured all the time," he said.
Denmark face a crucial finish to their Euro 2012 qualifiers as they are one of three teams at the top of Group H. Portugal are leading on goal difference from the Danes and Norway.
They will now have to plan without Agger for their final two qualifiers, away to Cyprus on October 7 and at home to Portugal four days later.
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