President Reagan yesterday made a strong plea for free trade in his regular Saturday radio address, declaring that America will lay out proposals for "limiting government intervention in world markets" at this week's meeting of trade ministers in Geneva.

The president yesterday also appeared headed for new conflicts with Congress over domestic spending,

Budget officials told Cabinet members Friday that the administration has tentatively decided to seek $25 billion to $30 billion in new domestic program cuts in the fiscal 1984 budget, sources said.

The cuts would be needed, the officials said, to help hold down the deficit.

Office of Management and Budget Director David A. Stockman reportedly told the Cabinet that without such cuts, the projected deficit would reach $185 billion to $195 billion.

Congressional leaders, who met with Reagan last week, told him then that big domestic program cuts were likely to face considerable opposition and were unlikely to pass.

Stockman already has made some initial decisions on how to allocate the cuts among broad general categories of programs, one source said, and Cabinet members will be getting guidelines this week.

The president, in defending the concept of free trade, said "exports account for over 5 million jobs in the United States. "Two out of every five acres planted by American farmers produce crops for exports."

At the Geneva talks, the United States is expected to press for steps to start curbing non-tariff impediments to trade.

While testing the microphone in preparation for the radio address, the president joked that the economy was in a "hell of a mess," news services reported, but that quip was not heard on the address as broadcast.

In another economic development, the president in a Friday telegram to the Natural Gas Supply Association renewed his support for natural gas deregulation, United Press International reported.