In his most pessimistic assessment since forming an interim government with internal black leaders, Rhodesian Prime Minister Ian Smith admitted yesterday that military efforts to end the five-year-old guerrilla war were not succeeding.

Speaking in a television interview, Smith appealed to the United States and Britain to resolve the situation with "one stroke of the pen" by accepting the agreement he worked out last March for qualified majority rule. This, he added, would lead to international recognition of Rhodesia, lifting of trade sanctions and an end to the war in the breakaway colony where blacks outnumber whites by more than 20 to 1.

"I concede that we are not succeeding as we had hoped. I am critical of our efforts so far," the Prime Minister said in the interview with British and Canadian television which was also broadcast in Rhodesia.

Smith's admission comes amid reports that the government is having increasing difficulties maintaining control in the countryside in the face of mounting guerrilla activity.

Earlier this month a spokesman for the Education Ministry said almost 750 schools in rural areas had been forced to close and another 63 had been burned down by the guerrillas, depriving about 208,000 black children of an education.

In the last week alone 30 schools serving more than 4,000 students had been forced to shut, he said.

Many of the clossings involve missionary schools. Four European missionaries were killed earlier this month.

Reuter reported from Salisbury that following the most recent killings the Anglican mission of St. James near Bulawayo shut after receiving a note from guerrillas saying, "if the school is not closed then there will be a smell of blood and it will be on your heads."

Diplomatic sources in Washington cited reports of a breakdwon of civil administration in rural areas with tax collections falling off. They also said hoof and mount disease and tsetse flies, long since wiped out, were once more evident in agricultural regions.

In his interview Smith said 20 persons a day were dying in the war and he indirectly blamed the United States and Britain for failing to support his plan worked out with the three internal leaders, Bishop Abel Muzorewa, Rev. Ndabaningi Sithole and Chief Jeremiah Chirau.

The Unted States and Britain are urging the internal leaders and the Patriotic Front guerrillas, headquartered in Zambia and Mozambique, to accept an Anglo-American plan which would turn administration of the former Britain colony back to Britain and end white control of the the security forces during the transition to black majority government.