President Reagan, declaring war on "a spendthrift, irresponsible bureaucracy," said yesterday that his administration is taking steps to save $168 billion by attacking waste, fraud and inefficiency in government.

On a day when his strides toward reducing huge budget deficits were attacked by governors as inadequate, Reagan hailed the work of his Private Sector Survey on Cost Control, better known as the Grace Commission after its chairman, businessman J. Peter Grace, for focusing national attention on government waste.

"Keep up the good work," Reagan told business executives who worked on the study. "Bring on the headlines about waste and fraud. The Grace Commission has led the way, and now it's everybody's fight."

The Grace Commission report has been criticized by the Congressional Budget Office and congressional Democrats as overly optimistic, and it has been adopted only in part by the administration. But it nonetheless has served as a rallying point for Reagan's exhortations against waste, fraud and abuse, a frequent refrain in his 1980 campaign.

Reagan said the administration has taken steps to implement 1,148 of the report's 2,478 recommendations, estimated to produce $56 billion in savings in his fiscal 1986 budget and $112 billion over three years.

At the same time, Reagan has kept at arm's length such other Grace Commission recommendations as cuts in military retirement benefits, shutdowns of military bases and changes in politically sensitive social-welfare programs.