A Cabinet minister and powerful political aide of Prime Minister Robert Mugabe was arrested today and charged with the murder of a white farmer in a move that is bound to test severely the fledgling Zimbabwe government.

Edgar Tekere, minister of manpower and the third-ranking leader in Mugabe's ruling party, was charged in the slaying Monday of Gerald William Adams, 68, manager of a farm 20 miles from Salisbury.

A brief police announcement said Tekere and "several other persons have been taken into custody and will appear before the courts in due course." The statement left unclear the motive or other details of the slaying.

Under Zimbabwean law, Tekere must remain in detention until his trial since there is no provision for bail in cases involving capital crimes. No date was set for trial. Unlike normal practice, Tekere was charged in a private hearing by a magistrate who was not identified.

Although the slaying appears to have been the result of an altercation, the trial of Tekere and his supporters, who reportedly were among the others arrested, could become an emotional focus of national debate on the moderate direction the country has taken so far under Mugabe.

The murder has touched a sensitive nerve among the 200,000 whites in Zimbabwe, many of whom believe that Mugabe's party and government officials have sometimes been above the law since the advent of black rule April 18.

For many blacks, Tekere is one of the heroes of Zimbabwe's 15-year struggle to end white-minority domination. He has criticized the government for acting too slowly in dismantling white privilege.

His arrest could cause a split in Mugabe's Zimbabwe African National Union-Patriotic Front party since Tekere has considerable following in his position as secretary general. In addition, Tekere is believed to have a strong following among the organization's 25,000 former guerrillas restively living in assembly camps awaiting demobilization or assignment to the new national Army.

Some of the guerrillas who support Tekere's hard line toward the whites and are anxious to receive the fruits of victory may consider the killing of a white farmer now as no different than what they had routinely been ordered to do during the seven-year guerrilla war.

The question is whether "the struggle continues," in the terminology of African revolution.

To many whites, whom Mugabe is seeking to keep in the country, Tekere's trial is likely to be a test of the rule of law and thus decide their future in Zimbabwe.

The trial is also likely to have international repercussions since Mugabe has been seeking Western investment and aid, which could be jeopardized if Zimbabwe is seen as moving in a vengeful way against the whites.

"The incident certainly tends to help those outsiders who have been portraying the country as falling apart" under black rule, said a Western diplomat, who said he believes that the first few months of independence have gone relatively well.

The police statement today added little to the sparse official information provided yesterday after Tereke was first picked up for questioning. It said that "during the course of further investigations, additional guns and ammunition have been recovered."

Yesterday police seized weapons from Tekere's bodyguards, reportedly to carry out ballistics tests.

Some officials said that the difficulties on the farm west of Salisbury began Sunday night when black former soldiers who had been part of the former white-led Army objected to noise coming from a party near the farmhouse allegedly attended by Tekere and two other ministers.

Tekere and his supporters reportedly returned to the farm Monday and the farmer was allegedly killed in a shootout with former soldiers.

A witness who said he was visiting the farm told the Herald, Salisbury's main daily newspapers, that the firing lasted "between 10 and 20 minutes," and that he identified a packed car that turned out to be Tekere's speeding away from the farm. Despite the amount of firing, Adams was the only known casualty.

Ralph Chadwick, who said he was a witness to the attack, told reporters he had seen "an extended sweep line" of armed men moving onto the Adams farm, Reuter reported.

The attackers fired at Chadwick, who was on adjoining property, and at the Adams farmhouse, Chadwick said. After a "final assault," he said, the attackers drove away. Police arrived shortly after, he said, and they and Chadwick found Adams, shot in the back, slumped over a two-way radio in the house, which had been badly shot up.

Because of the incident, Mugabe may face the dilemma of putting national interest ahead of the party, which technically is superior to the government.

A number of observers believe, however, that Mugabe's sweeping victory in elections last February has given him the clout to override recalcitrant elements in the party.

An aide to Mugabe said he has been "clearly disturbed" by the murder charge against Tekere and the potential impact.

The case has come at a difficult time for the prime minister, who is host to Mozambican President Samora Machel. the government has gone to great efforts to assure the success of the first state visit here.

Machel had given refuge to Mugabe's guerrillas since Mozambique's independence in 1975 and was regarded as the key outside factor in bringing about the end of white-ruled Rhodesia, which Zimbabwe has supplanted.

Machel made a fervent plea today for Zimbabwe to overcome divisive tribalism. Animosities between the majority Shona tribe and the minority Ndebeles have long plagued the country and have spawned separate political parties that, although technically united in a coalition government, often clash beneath the surface.

Accompanied by Mugabe and Patriotic Front leader Joshua Nkomo, Machel brought cheers from a rally in Bulawayo of both parties' supporters when he said that those who support tribalism are "an enemy" of the country.

Home Affairs Minister Nkomo, the father of the Zimbabwe liberation movement who had taken a backseat to Mugabe since the elections, was noticeably less enthusiastic than his rival about Machel's statements, witnesses said.

Meanwhile, P. M. Van der Byl, an outspoken white member of Parliament, said on the floor of the legislature that "the whole affair has become an international scandal" threatening to bring the government into disrepute.

Other members of the Rhodesia Front Party, which controls all 10 white seats in Parliament, sought assurances that the government would cooperate with police in the investigation and that the murder would not be "swept under the table."

Deputy Prime Minister Simon Mzenda, the second-ranking official in the party, said the "government will not suppress anything just for the sake of preventing things from coming out."

Police treated Tekere's arrest gingerly, questioning him at his home this morning and then allowing him to visit relatives before he presented himself at central police headquarters in midafternoon for further interrogation.

Almost five hours later, the statement announcing his arrest was issued.