The United States has begun a worldwide campaign to try to prevent the U.N. Convention on the Law of the Sea from going into effect.

The treaty, negotiated during the past eight years under Republican and Democratic presidents and about to be opened for signing at a ceremony in Jamaica this week, contains seabed mining provisions which the Reagan administration opposes.

As part of its drive against the treaty, the administration recently sent a special presidential emissary, former defense secretary Donald Rumsfeld, to visit five of seven "targeted" countries, according to State Department sources. Rumsfeld has tried to "convince leaders of the negative consequences of the treaty going into effect," the sources said.

Among the treaty's provisions are:

* The setting up of a multi-billion-dollar international undersea mining corporation that would automatically gain the exploitation rights to half of each site discovered by private consortiums and to which those private companies would have to transfer their mining technology.

* The taxes collected from future undersea mining could be distributed to less developed countries and even, according to Reagan officials, "national liberation movements" such as the Palestine Liberation Organization, which is an observer at the U.N. sea law conference.

* The United States and other major Western undersea mining countries would have only one-quarter of the votes on the international authority that would set the rules for the operation.

The task of halting the treaty will be formidable, because 130 nations at the last meeting of the U.N. conference in April voted to approve its final draft. Only the United States and three other nations voted against it.

This week, at the last week-long session of the conference at Montego Bay, Jamaica, delegates will make concluding statements and approve the "final act," a document that will officially end the eight-year negotiating conference.

On Friday, the treaty will be open for signing. After 50 nations sign the document, a preparatory commission is to begin drafting the regulations under which the treaty would operate. The treaty does not go into force until a year after 60 nations formally ratify it.

The initial American strategy, according to Reagan administration sources, is to try to keep the number of nations that ratify -- not sign -- the treaty below the 60 required to have it go into force. Washington officials expect that move to fail. "There are 45 nations in Africa alone," was the way one diplomat involved in the process put it yesterday, "and I can't believe they won't find 15 more."

Thereafter, officials said, they would work to convince "the main countries that would be involved in deep sea mining," such as the Western European allies and maritime nations, that "they should not become bound by the treaty."

Rumsfeld then started his mission, meeting on Dec. 1, with the new prime minister of Japan, Yasuhiro Nakasone. Nakasone "said he would study the possibility of not signing the treaty in Jamaica," a U.S. diplomat said.

American officials point to other recent gains. Britain came out against the treaty last week, and the new West German government is said to be heading toward the same decision.

Although the French government said last week it would sign the treaty, American officials said they had been assured the treaty would not be ratified by Paris "in the near future."

State Department sources said they were also hopeful that many Latin American countries will decide to hold back from either signing or ratifying the treaty. Venezuela already has said it would not sign, and Peru is expected to follow.

The United States also has taken the lead to limit available U.N. funds. A U.N. secretariat staff plan to fund the preparatory commission at $20 million was U.S. leaked to American reporters. After the resultant publicity, the budget was sliced to $4.2 million.

Last Friday, the deputy U.S. representative to the United Nations, Kenneth Adelman, proposed to the General Assembly that those nations that sign the treaty be required to fund the preparatory body. Without such a provision, the United States, which opposes the treaty, would have to put up about 25 percent of the commission's operating funds under the normal U.N. funding allocation system.

Adelman's motion lost by a 134 to 3 vote. In addition, a resolution by treaty supporters, directed at the United States and calling on all members to refrain from "undermining the treaty or defeating its object and purpose," was approved by the same 134 to 3 vote, with the United States voting against it.

American opposition to the treaty did not emerge until the Reagan administration took power. Up to that time, U.S. diplomats had played a key role in the eight years of negotiation. In fact, in 1976, then secretary of state Henry A. Kissinger authored a key provision of the treaty that today is the focus of much of the Reagan team's opposition.

Up to that time, the less-developed countries had demanded that any exploitation of the natural resources below the sea should be done entirely by an international organization controlled through the United Nations. Kissinger broke the deadlock by coming up with what is termed "parallel access."

Under Kissinger's plan, private companies would be allowed to search for undersea mining sites. When they found one, it would be divided evenly between the company and the U.N.-created body.