Singh, who arrived here to take stock of the situation, said he understood the "shock and outrage" of the people of Mumbai and "I share their pain, anguish and anger".
He said he had announced ex-gratia payment of Rs two lakh each to the kin of those killed and Rs one lakh each to those injured from the Prime Minister's National Relief Fund.
"I cannot find words to condemn the barbaric acts of terror that resulted in the senseless killing and injuring of innocent people in Mumbai," Singh said in a statement as he arrived here accompanied by UPA Chairperson Sonia Gandhi.
"I have come here in solidarity with the people of Mumbai," he said while extending his "deepest condolences and sympathies to those who suffered in the terrible tragedy".
Singh said he had asked Union Home Minister P Chidambaram and Maharashtra Chief Minister Prithviraj Chavan to continue to coordinate their efforts and resources to "relentlessly pursue the perpetrators. They must be brought to justice quickly and be subject to the rule of law that they have sought to subvert."
He sought the cooperation of all citizens in this effort, saying "we owe this" to the grieving families. He also assured the people that "the government will do everything in its power to prevent such attacks in the future."