President Carter has earmarked $13 million in his new defense budget to start the controversial communications system in Michigan and Wisconsin for sending messages to submarines in the depths, administration sources said yesterday.

The communications net, called ELF and formerly named Sanguine and then Seafarer, has been successfully opposed for years by environmentalists and politicians in Michigan and Wisconsin. Carter last week told politicians from that area that he would continue to study the need for ELF even though money for it would be included in the fiscal 1980 budget.

The Navy has been contending that a new communications network is vital to enable the submarines to remain submerged and safe from detection when they receive messages from shore. Currently, submarines on duty must rise near the surface of the sea and send out a trail of wire to receive messages, risking detection.

Environmentalists have argued that the risks to plant and animal life from the land emissions are unacceptable, and that alternatives to the network have not been adequately explored.

The system envisioned in the Carter budget would consist of comparatively small sites. One is in Wisconsin, near Clam Lake, already a test site for the grid, and the other is in Michigan's Upper Peninsula, mostly on Air Force property. The two sites would be connected.