Prime Minister Mugabe today ordered the deployment of units of the integrated Zimbabwean Army to crush mounting violence that has swept the newly independent African nation.

Speaking sternly in a nationwide television and radio address, Mugabe said, "The evil elements must be routed and routed with speed."

He said the troops will be deployed in conjunction with the police in and around Salisbury, the capital, and two other cities but warned, "If need be, more forces will be deployed to cover more areas."

The outbreak of lawlessness has stirred fears among the population's already nervous 200,000 whites and could effect promises of much-needed Western investment.

The move, Mugabe's first against the outbreak of lawlessness, will be a test of the discipline and professionalism of the newly formed national Army. The Army, which so far has four 1,000-member battalions, is made up partially of elements from former guerrilla units that supported Mugabe and his junior coalition partner, Joshua Nkoma. The other portions of today's Army are members of what was the white Rhodesian Army until the country's independence.

Much of the violence has been attributed to dissidents from the two guerrilla armies. Many have become disgruntled while awaiting nine months at distant assembly points to claim the benefits of black-majority rule after fighting for years to end white domination in the nation formerly known as Rhodesia.

Thus, the soldiers will be asked to take action against men who, until recently, were their comrades in arms.

In the last two weeks there have been a number of incidents of political violence around Salisbury. In one a white farmer was killed and in another a white woman shot and killed a dissident guerrilla attacking her farm.

Last weekend a grenade was thrown into an African bar in the mainly white suburb of Mabelreign, five miles from downtown Salisbury. The bar was then machine-gunned by the unidentified assailants, resulting in two deaths and 25 injuries.

Fifteen hundred heavily armed guerrillas tasted their first fruit of victory today as the government moved them from an assembly point near the Mozambique border to a housing settlement on the outskirts of Salisbury.

The guerrillas, members of Mugabe's Zimbabwe African National Liberation Army, brought with them all their armaments, which included Soviet-made AK47 rifles, rocket-propelled grenades, mortars, bazookas and bayonets.

"They've got everything," said the head of the military police escort for the 58-vehicle convoy.

The action is a calculated gamble by Mugabe that moving thousands of guerrillas from their remote camps, established during the British-administered cease-fire that led to independence, to build-up areas will bring them back into the mainstream of life and reward them.

The government also apparently hopes that living near the city will encourage many of the troops to give up the military for civilian life.

In the aftermath of a seven-year war that did not result in a military victory for either side, the country is left with about 35,000 guerrillas and 10,000 soldiers from the former Rhodesian Army. The new integrated Army will probably be able to absorb only about a third of this total, but the guerrillas have been loathe to give up their uniforms since for many it is the only life they have known.

Bringing the heavily armed guerrillas into populated areas could lead, however, to an increase in the type of violence that Mugabe sought to stamp out today.

The prime minister instructed the military units deployed "to restore law and order by rounding up all dissident elements and taking possession of all illegal weapons."

Shaking his finger, Mugabe said, "I have repeatedly warned those concerned of drastic measures against them by government unless they desist from the folly of their barbarous acts, lawlessness and undisciplined behavior."

He then made a cryptic reference to "the insidious activities" of "irresponsible political leaders," saying the government is watching them very closely.

"Leaders who deliberately defy the law court the wrath of the law into themselves," he warned.

No details were given of the political leaders to whom he was referring. The remark could be taken to mean members of Nkomo's Patriotic Front party opposed to their alliance with the government or possibly to Mugabe lieutenant Edgar Tekere, who is free on bail awaiting trial on a murder charge.

Before and since his arrest, Tekere, secretary general of Mugabe's political party, has been critical of the government for moving too slowly in changing the country's white-dominated structure. Many of the guerrillas in the assembly points are believed to support Tekere.

The guerrillas who made the 150-mile trip in a slow convoy today were greeted along the route by cheering crowds. About 3,000 chanting demonstrators were on hand to greet them at their destination, the sprawling Chitungwiza township about 12 miles south of Salisbury.

Shaking their fists and obviously feeling they were finally being rewarded for their battle efforts, the guerrillas shouted in unison, "We have fought the war." The crowd, mainly women and children, chanted, "Welcome comrades, you have come for good."

One guerrilla, holding a 60-mm motar tube, said, "I have suffered for the masses and now I have come home."