The Italian government is desperately trying to wriggle its way out of implementing sharp curbs in its steel production demanded by the European Community that would leave tens of thousands here unemployed.

With a summit meeting of European industry ministers scheduled for July 25 on the steel issue, the Italian government is seeking to work out a strategy to convince Brussels to pare down its demands for cuts in Italy's steel-producing capacity equal to 5.8 million tons.

The Italian government's official reaction so far to the steel cuts ordered at the end of June is that they are "unacceptable, inapplicable and wasteful."

There has been talk of an appeal to the European court of justice and threats of retaliation though an Italian veto of a European coal and steel emergency regulation that must be extended to permit the European Community to fix national steel-production quotas for the coming year.

But these measures appear primarily to be the opening gambits in an Italian bid for renegotiation of its community steel position. An industrial recession is in full swing at present in Italy and with steel consumption down 22 percent in the first quarter of 1983. Italian financial ministers feel the cuts called for by the community would be politically impossible to implement.

According to Giorgio Falck, head of one of Italy's leading private companies, it would be possible to find new jobs for an estimated 40,000 people who could be affected by the cuts. But the Italian trade unions are strongly opposed to implementing the community's demands, and the Socialist State Industry Minister, Gianni de Michelis, already has promised that Cornigliano, the large state-run steel plant near Genoa, will definitely not be shut down as could become necessary if Brussels' instructions were to be followed.

Last week Italian Foreign Minister Emilio Colombo met at length in Brussels with Industry Commissioner Etienne Davignon and Economics Commissioner Francios Xavier Ortoli in an attempt to get new negotiations rolling. And Italian Industry Minister Filippo Maria Pandolfi traveled to Brussels yesterday for the same purpose.

But so far the community has shown no willingness to compromise. The cuts demanded of Italy are part of a total package calling for a reduction in European steel production by a total of 26.7 million tons and changes in the Italian quota would mean upping the burden imposed on other countries.

The fact is that there is little sympathy in Brussels for the Italians.

Since 1974 when overproduction and a shrinking steel market first led to concern about the sector's future, the Italians----who last year produced 24 million tons or 0.8 percent more than in 1974--have eliminated only 4,000 jobs from the steel industry out of a total of 300,000 in the community as a whole.

The plan proposed for cuts of 2.6 million tons by Finsider, the heavily indebted Italian steel company, was judged inadequate in Brussels. The community's response was to order that 4.8 million tons be cut by Finsider and another million by Italy's private-steel producers for a total of 5.8 million tons.

The community has offered no specific blueprint for implementing the cuts but Italian industry experts say that, to follow through on community instructions, production would have to be halted not only at smaller Finsider plants in Terni and San Giovanni Valdarno in Central Italy, Marghera near Venice and Campin near Genoa, but also at Cornigliano, where hundreds of workers are already on short-time.