Consumer activist Ralph Nader accused General Motors Corp. yesterday of embarking on an "avaricious" campaign to pressure local governments to reduce their property tax assessments of GM plants, warehouses and other facilities.

Within the last month, GM has sought property tax reductions of 30 to 70 percent in at least 12 Michigan townships and counties, according to a survey of 20 local governments by Nader's Center for the Study of Responsive Law.

GM said in a statement that it is "seeking to have its property tax assessments reduced in several jurisdictions in Michigan and other states," but the company would not say how many jurisdictions are affected, or where they are located.

The company also would not disclose the amount of money it pays in property taxes or the amount it hopes to save through lower assessments, but a spokesman said GM paid $222 million in Michigan real, personal and property taxes in 1983.

GM's statement said that international competition has forced the world's largest auto manufacturer to review more closely "its costs of doing business, including the cost of real property taxes."

It said its "internal studies and advice from independent experts indicated that many assessments of our property around the country substantially exceed lawful amounts based on fair market value."

Nader said his research group had contacted 20 local governments in Michigan, 15 of which said they had received GM property tax assessment appeals. Of those, 12 jurisdictions said GM had requested specific assessment reductions, he said during a meeting with reporters.

Although unable to estimate how many towns may be affected, Nader said his group thinks its survey reflects "the tip of the iceberg," both in terms of GM's efforts and the encouragement it gives to other companies that might follow suit.

GM has "initiated an avaricious assault on the fiscal well-being of cities and towns across Michigan," Nader said in a letter to GM Chairman Roger B. Smith.

The auto maker said it hopes to resolve any disputes "at local levels if at all possible, keeping in mind the impact of GM tax revenues to the communities in which we operate."

William B. Ayre, supervisor of Genesee Township, Mich., said GM's proposed assessment reduction would be "a severe blow" that would "bankrupt the local school." GM has proposed a 59 percent cut in the town's real-property assessment of GM's Fisher Body plant to $10 million from the current level of $24.5 million, Ayre said.

GM currently pays about one-fifth of all property taxes in Genesee, Ayre said, estimating that the school system and township combined would lose future revenue of $880,000 a year. If GM prevails, the community also would have to refund past overpayments of taxes plus interest, he said.

Other towns and counties where GM has filed assessment appeals include Lansing Township, Pontiac, Saginaw and Flint, Mich.