WASHINGTON (AP) _ Business magnate J. Peter Grace is spending $2 million in advertising this year to lobby Congress into passing $424 billion in federal budget cuts proposed by a presidential commission he headed in 1983.

Most of the money is being spent on half-page newspaper advertisements urging people to demand that their senators and representatives reduce the federal deficit, Grace spokesman Tony Navarro said Wednesday.

The ads, which started running earlier this week in The New York Times, The Washington Post, USA Today, and The Wall Street Journal, list all senators and representatives from the 50 states under the message:

''If the deficit goes down, here's who to thank. If it goes up, here's who to replace.''

At the bottom of the ad is a clip-out coupon designed to be mailed to members of Congress and bearing the warning: ''Please bring down the deficit now. If you don't, I'll vote for someone who will.''

Navarro, a vice president for the New York-based W.R. Grace & Co., said the ads will run through the summer while Congress debates the 1986 federal budget.

''Our interest is both altruistic and selfish,'' Navarro said. ''If the country's economy veers out of control, we are all going with it. This campaign is an investment in the country's future.''

Last year, Grace spent $2.6 million on a television and print ad campaign featuring a crying baby to rally support for federal spending cuts. The ad, which some members of Congress said generated a moderate amount of mail, showed a newborn American infant bawling as she is told she is entering the world owing a $50,000 share of the federal debt.

Grace, 71, turned to advertising after Congress criticized the presidential commission's 1983 report as too simplistic. The Congressional Budget Office and General Accounting Office have said the panel's proposed savings were exaggerated and that in many cases couldn't be implemented because they required sweeping policy changes.

Grace commission ideas include using more outside contractors to do federal work, reducing welfare payments, limiting some Social Security benefits, and tightening the Defense Department's bidding system.

The panel said implementation of all its recommendations would produce a 31 percent reduction in federal spending by the year 2000.

Citizens for Tax Justice, a Washington-based public interest group, has reported that from 1981 to 1983, W.R. Grace offset $40.5 million in federal taxes with the $53.2 million in federal tax credits.

Navarro said, however, that those tax credits were deserved because the company suffered losses in its fertilizer and farm-related industries. He said the company paid $14.3 million in federal taxes in 1984.