Rhodesia's black and white leaders launched a major diplomatic offensive yesterday to convince the West and Africa that the internal agreement they have just signed for a transition to black majority rule is worthy of international support.

Their task, however, is a formidable one. Even as they embarked on their campaign to gather support for the agreement among the Western powers - particularly from the United States and Britain - five small bomb explosions jolted parts of Salisbury.

No one was injured by the blasts, and it was not known who was responsible. Immediate speculation, however, focused on black nationalists loyal to the "Patriotic Front" guerrilla movement, which yesterday denounced the internal settlement plan as "completely bogus."

But Prime Minister Ian Smith and the three black leaders who signed the agreement Friday hope to persuade the West that their plan to establish majority rule in Rhodesia by Dec. 31 warrants a decision to lift the U.N. economic sanctions that were imposed a decade ago against the breakaway British colony.

Within hours of the formal signing ceremony Friday, Smith was appealing on television to the United States "to give us a helping hand instead of trying to hinder us as they [the Americans] have heretofore."

He asked President Carter to lift the sanctions and help arrange a cease-fire, presumably by pressuring the five frontline African states to end their backing for the Soviet-armed Patriotic Front, the alliance of two guerrilla forces waging the war inside Rhodesia.

Even before Smith made his appeal, Bishop Abel Muzorewa, leader of the black United African National Council, had left for London to sell the agreement to the British government. He may travel on from there to Washington for the same purpose.

Following shortly will be the Rev. Ndabaningi Sithole, head of his own African National Council, who plans to spend two weeks in the United States, while Chief Jeremiah Chirau, leader of the third black party to the agreement, is scheduled to go to Western Europe.

At the moment, there is little interest in Salisbury in the British-American proposal for new negotiations between the new multiracial, internal government and the Patriotic Front to bring the guerrilla leaders into an overall settlement.

"I rule it out altogether," said Sithole in an interview. "The question of merging the internal and external plans does not arise. The marriage has already been consummated," he said, referring to the agreement just signed by Rhodesia's internal black and white leaders and the rival Angola-American proposals for a settlement.

The British and American governments had been holding their own negotiations with the Soviet-backed Patriotic Front alone before an agreement was reached in Salisbury. The two Western powers are now anxious to find some way of bringing the Front together with the internal leaders to assure an end to the guerrilla war and also avoid another Soviet-American confrontation in Africa.

Rhodesian government sources echo Sithole's view, saying, as Smith did Friday, that the Front's coleaders, Joshua Nkomo and Robert Mugabe, are welcome to return and join the interim government. But they see no reason for negotiating a whole new agreement with the Front.

To sell this "no compromise stratsians hope to "rehabilitate" to respectability the old five-point peace plan for Rhodesia proposed in 1976 by Secretary of State Henry Kissinger. They say the internal agreement just egy" in the United States, the Rhode-signed was patterned largely after the Kissinger plan.

They also argue that since the Kissinger plan was endorsed by President Carter just after his election, he should therefore back the present Salisbury agreement.

The Kissinger plan called for Smith to accept majority rule within two years and to set up a mixed interim government with a white-led council of state and a black-chaired council of ministers. In return, Kissinger promised Smith that the economic sanctions imposed by the United Nations in 1965 would be lifted once the interim government was established. The guerrilla war was also supposed to cease.

The internal Rhosesian plan has in fact fulfilled these basic principles and even met the Kissinger timetable for establishing a black majority government - the end of this year. But there are also important differences.

The Kissinger proposals did not provide for Smith to remain as prime minister during the transitional period or for the present white-dominated Parliament to continue functioning as it will under the agreement just signed.

Equally significant, the Patriotic Front, as well as Muzorewa and Sithole, rejected the Kissinger plan at the abortive Geneva conference on Rhodesia in late 1976. They found it too vague and favorable to the whites, although ironically the agreement Muzorewa and Sithole have just signed is probably even more so.

The Rhodesian strategy also counts heavily on the three black internal leaders to gain the backing of a majority of African states for the agreement. Both Muzorewa and Sithole sent aides to the recent meeting of the Council of Foreign Ministers of the Organization of African Unity held in Tripoli, Libya, to argue their case.

While the conference refused to allow the aides to speak and voted to continue the African organization's policy of backing the Patriotic Front, Muzorewa and Sithole were encouraged by signs of support from at least eight states.

Sithole's information secretary, Abel Rumano, listed the following countries as showing sympathy for an internal settlement: Zaire, Uganda, Somalia, Sierra Leone, Sudan, Mauritania and Liberia. In addition, Kenya, Senegal, Gabon, the Ivory Coast and Botswana, a frontline state, are regarded as probable supporters.

More interesting, if true, Rumano estimated that Tanzania and Mozambique, key backers of the Patriotic Front, were among 36 African nations "sitting on the fence."

He named only five countries - Zambia, Ethiopia, Algeria, the Congo, and Angola - as dead set against recognition of an internal settlement.

Some outside observers here regard the Rhosesian "no compromise strategy" as fundamentally weak unless the country's internal leaders can show, as they claim, that they have the majority of 6.7 million blacks on their side through some kind of public opinion poll.

There is no enthusiasm in Salisbury for holding a nationwide referendum, but neither is it being excluded if, as Muzorewa said Friday, "We discover that it is necessary to have to do that."

Both he and Smith said the new executive council heading the interim multiracial government would decide this, presumably depending on whether the British and American governments demand one before endorsing the internal agreement. Another possible test of its acceptability to the black population being discussed is a survey of public opinion by a neutral outside commission. The British ran a survey of this kind in 1971-72 on a British-Rhodesian settlement plan.

After touring the country to listen to black views and collect written statements, the Peace Commission, as it was known, found that the plan was unacceptable to the majority.

Although the white minority Rhodesian government was furious with the findings, it is not impossible that it would prefer another commission to a referendum, as voting under present guerrilla war conditions would not be easy.

But perhaps the best test of acceptability will come from the battlefield itself. Sithole said Friday that the agreement the three black leaders had just signed was "on behalf of the guerrillas," and that the "overwhelming majority" of them would back it.

"We will got out and tell the guerrillas that what we have been fighting for had now been achieved . . . I know for sure that they will come back home, they will lay down their arms," he said.

Whether he is correct in this prediction should become evident shortly and so, too, should the need, or lack of it, to negotiate with the Patriotic Front.