The visit here of a world-touring South African rugby team has transformed the fields of New Zealand's most popular sport into battlegrounds and created an international backlash that is threatening to extend to the cuntry that will be the South African's next host -- the United States. After only three matches of a 16-date tour lasting until mid-September, opposition to the government's admission of the renowned Springboks rugby team has forced the cancellation of one game because of a riot and endangered New Zealand's standing in two United Nations committees and the Commonwealth, which recently voted to move a coming meeting of finance ministers from Auckland to the Bahamas in protest.

Meanwhile, 15 Commonwealth members, led by black African nations angered by New Zealand's refusal to halt the tour because of Sout Africa's racial policies, have called for New Zealand's exclusion from the 1982 Commonwealth Games in Australia.

Now, as the Springboks prepare to play New Zealand's equally prestigious national rugby team, the All Blacks, after a series of matches with provincial teams, the issue here has turned from which side will win to the new role of rugby in the nation's politics and foreign relations.

That debate appears likely to surface in the United States when the Springboks arrive in late September for a tour of three cities. Britain's sports minister, Hector Monro, said this week that the 1984 Olympic Games scheduled for Los Angeles could come "under threat" if the tour continues as planned, and it has been noted here that black African nations boycotted the 1976 Olympics in Montreal because New Zealand was not excluded for allowing its rugby team to tour South Africa.

In Washington, State Department officials said that U.S. laws governing visas contain no provision that would permit the administration to prevent the Springboks' tour, which is being sponsored by the U.S.A. Rugby-Football Union.

["The fact that it is not the most popular thing for the government to do is not provided for in the law," said spokesman David Nall. "We reviewed the applications and concluded we had no choice under the law but to grant the visas."]

In New Zealand, internal unrest has matched the international repercussions. Traditionally nonviolent New Zealanders, many of whom have never seen a police officer with a nightstick in his belt, now find themselves calling on police to pummel other New Zealanders to prevent further disruption of the tour.

As these thin blue lines of police try to prevent pitched battles between avid rugby supporters and antiapartheid protesters around the country, Army and Air Force personnel and equipment have been called in to give logistical support. The first estimated cost to the police of keeping the peace was $2.3 million -- compared to the $2.5 million the private Rugby Union expected to make from the tour -- and the security costs are escalating daily.

[Prime Minister Robert Muldoon said today that he is considering an early election on a law-and-order issue because of the violent rugby protests, Reuter reported. New Zealand's general elections are scheduled for November. Muldoon also said he has called a meeting for Monday to discuss the possibility of cutting short the Springboks' visit because of the disruptions.]

The controversy is all the more heated in New Zealand because the rivalry began here 60 years ago, when a South African rugby team toured the country and tied a series with the All Blacks, a national team that draws its name from the color of its uniforms. Competition has flourished between the two nations ever since, and for the past 30 years, the clashes have been haunted by the specter of apartheid.

In 1949, as the All Blacks prepared to leave for a tour of South Africa without the players who were Maoris, or ethnic Ploynesians, some New Zealanders took tot he streets to demonstrate with placards that read, "No Maoris, No Tour." The tour went on anyway, but in 1967, the government said that if Maoris could not go abroad, the team must stay home. Since then, Maoris have played on teams in South Africa.

The Springboks visited New Zealand in 1956 and 1965 and wre due here again in 1973, by which time black Africans and others were trying to isolate South African sportsmen. All through the 1972 election campaign, debate raged over whether New Zealand was encouraging apartheid by playing rugby with the Springboks, or was educating South Africans by showing them that Maoris were treated as equals.

Finally, the Labor Party came to power and the new prime minister, Norman Kirk, resolved to break a preelection promise to allow the South African rugby players to come. He said he changed his mind because the police had advised him they did not think they could control the many New Zealanders who had vowed to protest the visit.

The South African team was an election issue again in 1975, and the present prime minister, Robert Muldoon, said that not only would the Springboks be allowed to tour, but the government would welcome them. The All Blacks subsequently went to South Africa in 1976 -- and African nations ended up staying home from the Montreal Olympics.

In the wake of the boycott, Muldoon was persuaded by Commonwealth leaders to sign what has come to be nown as the Gleneagles agreement, which committed Commonwealth goverments to taking steps to stop sporting contacts with South Africa. Now, Muldoon stands accused of breaking that compact -- a charge he hotly disputes.

Muldoon says he had always made it plain he would not refuse to issue visas to any sportsmen, adding that he has tried to persuade the country's Rugby Union to halt the tour. Meanwhile, union officials say it is not their job to administer foreign policy, and if the government will not ban the South Africans, the Rugby Union will not, either.

Other New Zealanders are split roughly down the middle on the Springboks issue. The heads of the Anglican and Roman Catholic churches -- the two biggest in the country -- have come out sternly against the tour. A number of high schools have dropped rugby, while others have said they would allow pupils time off to see midweek matches. And the Maoris are also split, some firmly denouncing the tour, some adamantly favoring it.

At the first game last month in the east coast city of Gisborne, the Springboks were welcomed to the Maori meeting house and the few demonstrators were dealt with by police, unarmed as usual.

But at Hamilton, the North Island dairy farming center where the Springboks were due to play the champion team Waikato on July 25, a group of about 300 protesters burst through a fence just before the match was due to start, invaded the field, linked arms and refused to move. Outside, 26,000 rugby supporters glowered as about 500 police, some in riot helmets and carrying nightsticks, confronted them.

The police began arresting the passively resisting protesters, but the match was canceled an hour after it was due to begin because police were told that a protester in a stolen plane intended to crash into the grandstand. The plane was forced to land, but as police escorted the protesters from the field, New Zealanders watching television saw mob violence as rugby fans punched protesters and police and hurled beer cans at point-blank range.

The mob violence was followed by an angry reaction. Police were accused of being too soft, and a South African police commissioner boasted he could have handled a mere 300 protesters with only 20 men. To that, a top New Zealand police officer snarled, "Given his bloody system, I could have done it with less."

Now, both the protest and the fury of rugby lovers are gathering momentum. Most observers believe that the confrontations will grow worse, and many fear the kind of violence and death that they have only read about until now.

The government and the Rugby Union remain adamant, however, and while the fight continues on the playing fields, the international reaction to the tour has been growing.

In addition to causing the switch of the Commonwealth finance ministers meeting and endangering New Zealand's place in the 1982 Commonwealth Games, the tour has created a gulf betwen New Zealnd and its most important trading partner, Australia, with whom it is now trying to form a common market.

The Australians had their own demonstrations during a South African tour in 1971 and now Australia will not even allow South African athletes to pass through on their way to New Zealand. To make the trip, the Springboks had to travel by wayof the United States.

New Zealand was hoping to represent the Western European nations on the U.N. Security Council next year, but informed sources consider the nomination now unlikely because of reaction to the tour. The country's candidacy for the U.N. International Law Commission has similarly been jeopardized.

Muldoon has reponded to these developments by saying he would have the human rights record of some of the black African countries put on the agenda for the Commonwealth prime ministers' conference in Melbourne in October.