Thousands march in Khartoum venting anger over drawings in Danish newspapers.
However, she said Denmark would not cut its development aid to Sudan, an idea she had floated earlier on Thursday.
She said: “Our support is not a support to the Sudanese president or, for that matter, to the government.
“It surprises me that Sudan’s government apparently is willing to cut the cooperation with a donor like Denmark on development aid because of a caricature in Danish newspapers.”
Such a move would affect “the most vulnerable groups in their own country,” she said.
The aid minister said she had summoned Sudan’s Norway-based ambassador to Denmark for a meeting, saying there was a “great need for an elaboration” on the statement made by al-Bashir.
After Sudan’s government and southern rebels signed a peace agreement in 2005, international donors said they would look into the country’s debt relief.
Sudan is one of the largest recipients of Danish aid.
In 2006, Khartoum received $26m from Denmark and a $100m humanitarian and reconstruction package is planned through 2009.
Newspapers in Denmark reprinted the cartoon showing Muhammad wearing a bomb-shaped turban with a fuse on February 13 to show their commitment to freedom of speech after Danish police said they had uncovered a plot to kill the artist who drew it.
The reprinting sparked protests in several Muslim countries.
The drawing was one of 12 cartoons, first published in a Danish newspaper, that triggered major protests in Muslim countries in 2006.