"The Secretary-General (Ban) condemns the attacks that have killed and injured many in Mumbai," said a statement from his office.
"No cause or grievance can justify indiscriminate violence against civilians. The Secretary-General expresses his solidarity with the Government and people of India, and extends his sincere condolences to the families of the victims," it added.
The UN Security Council also "condemned in the strongest terms" the bombings.
They expressed their deep sympathy and sincere condolences to the victims of these "heinous acts" and to their families, and to the people and Government of India.
"The members of the Security Council reaffirmed that terrorism in all its forms and manifestations constitutes one of the most serious threats to international peace and security, and that any acts of terrorism are criminal and unjustifiable, regardless of their motivation," a statement read by Peter Wittig, Germany's ambassador to the UN and current Council president, said.
Terror struck Mumbai last evening when three near simultaneous blasts ripped through crowded areas in the city. At least 21 people were killed and 141 injured.