The Communist Party will tackle critical food shortages in a special meeting this week that comes amid signs President Mikhail S. Gorbachev and Politburo rival Yegor K. Ligachev disagree on the solution.

The hottest issue on the agenda of the 300-member Central Committee is Gorbachev's desire to lease state-owned fields to farmers.In recent appearances, Ligachev has skipped lightly over leasing and emphasized collective farming - the traditional system that has left Soviet consumers standing in line for meat and vegetables.

At the meeting Wednesday and Thursday, the policy-making Central Committee is likely to agree on the need to ease the poverty and isolation of rural life. It also is expected to order the dismantling, at least partially, of an agricultural superministry formed in 1985.

In what appeared to be part of a campaign leading to action against the superministry, the Communist Party daily Pravda on March 6 reprinted citizens' complaints the agency is bureaucratic, ineffective and useless.

The Central Committee also will formally elect the 100 Communist Party members nominated for the nation's new 2,250-member Congress of People's Deputies.

But the meeting's major task is to overcome divisions at the highest levels and to take bold action on the worsening shortages that could derail Gorbachev's entire reform program.

The "food problem," as it is known in the Soviet Union, means:

-Long lines for limited products of poor quality.

-A diet that includes twice as many potatoes and 50 percent more sugar than Americans eat, but roughly half the fruit and meat.

-A distribution system that lets three out of four potatoes rot before they reach the table.

-A grain harvest of 195 million tons in 1988 - well below targets - that required the Soviet Union to spend precious foreign currency to import 36 million tons.

-Migration to the cities to escape the inadequacies of rural education, housing, roads, goods and services.

"Today, comrades, the most critical question is, unconditionally, supplying the population, normalization of the demands of the market," Gorbachev said in a speech in Kiev last month.