Prime Minister Robert Mugabe, faced with mounting internal political unrest, today set March as his target date for the country's first national election since Zimbabwe achieved independence five years ago.

Mugabe told Parliament he regretted recent demonstrations by his supporters in several areas that have resulted in violence and hobbled efforts of opposition leader Joshua Nkomo to campaign publicly.

But while he urged restraint, Mugabe added that such demonstrations were a "natural reaction and response" to the recent murders of several officials and members of his ruling party by armed dissidents he contends are loyal to Nkomo.

"Who is doing the greatest violence to our constitution? . . . Certainly not my party," said Mugabe. "We regret those demonstrations which are violent but in most cases they have been provoked." He added of Nkomo's Zimbabwe African People's Union, "They must stop killing our members."

Nkomo was forced to flee the southern city of Masvingo 12 days ago after pro-Mugabe demonstrators stoned his bulletproof car. The opposition leader also said shots were fired at his car, an allegation police have denied. Minister of Home Affairs Simbi Mubako has ordered a police investigation into the incident.

Police canceled another Nkomo rally last weekend in the northwestern town of Chinoyi after five persons were injured during demonstrations against his visit.

Nkomo said at a recent press conference that the attacks were part of an organized effort by Mugabe's ruling Zimbabwe African National Union to conduct a campaign of terror against him and his supporters. He vowed, however, to continue campaigning.

"I am going to travel wherever I want in this country," said Nkomo, who has deplored murders by armed dissidents and denied any link to them. "No one is going to stop me and I expect protection."

Mugabe, who captured 57 of 80 contested parliamentary seats in the preindependence election in 1980, is widely expected to retain a ruling majority. Under the national constitution, 20 other seats in the governing body are reserved for white voters until 1990.

Nkomo, who won 20 seats in 1980, has charged for months that the government's crackdown against dissidents in the southern Matabeleland region -- Nkomo's political stronghold -- has terrorized residents of the region and made it impossible to hold a fair election. Mugabe's supporters in turn have charged that dissident activities in the region are designed to force residents to support Nkomo against their will.

According to the government, 58 civilians were murdered by dissidents during the second half of 1984, including one top official each from the ruling and opposition parties.

The government has reported two more civilians associated with the ruling party have been killed since New Year's Day. Michael Sibanda, a district chairman in the northern Matabeleland town of Nkayi, was murdered nine days ago by three unidentified men who the government contends are dissidents. Another party member reportedly was killed and nine seriously injured by rebels last weekend in the southern Tjlotjo area.

Like Mugabe, some senior ruling party members have publicly urged restraint. Minister of Transportation Herbert Ushewokunze, a member of the party's ruling politburo, last week told an interviewer from the state-operated Herald newspaper here, "If you ignore Nkomo he gets smaller and smaller. If you react viciously he gets bigger and bigger. The best form of violence against Dr. Nkomo is to vote heavily against him."

Minister of State for Political Affairs Maurice Nyagumbo, another influential politburo member, told the funeral gathering for Sibanda last weekend, "We want to wipe away Nkomo in the forthcoming general elections. Anybody who will dare to lift him up after that will face the music."