The Rhodesian government announced triumphantly tonight that the turnout of black voters had reached 57 percent, with one day still to go in elections for Rhodesia's first black-led government.

Indications were that the final turnout will surpass 60 percent, with nearly 1.7 million of the 2.8 million blacks having voted already.

The turnout appeared to strength the current white-dominated government's positive as it again seeks to obtain diplomatic recognition, primarily from the United States and Britain.

Addressing a large crowd of international observers and correspondents, Prime Minister Ian Smith declared that events were going "very well" and asked the West, "What more do you want us to do?"

He said Rhodesia now had met all of ther terms that Britain and the United States had ever laid down in their various peace plans as preconditions for recognition and a lifting of economic sanctions and that it was time to stop applying "double standards" to Rhodesia.

"I would have thought that 50 percent would have satisfied any fair-minded person," Smith said, nothing that Rhodesia was in the midst of a war. He pointed out that less than 40 percent of Americans voted in last November's congressional elections. The actual American turnout was 35 percent.

A nine-man delegation from the New York-based Freedom House, which is here to monitor the elections, issued an interim report saying that despite some shortcomings, "the country has never had so inclusive and free and election.

"The elections in most underdeveloped countries are less free," it said.

"In a world in which peaceful change does not and cannot occur all at once, this election is a useful and creditable step toward the establishment of a free society in Zimbabwe-Rhodesia."

The delegation is led by Leonard R. Sussman, Freedom House executive director, and includes the black civil rights leader Bayard Rustin and the former U.S. representative to the U.N. Human Rights Commission, Allard Lowenstein.

At a news conference, Rustin called the elections a "first vitally important step toward a possibility of peace in SOUTHERN AFRICA." DEFENDING THE NEW RHODESIAN CONSTITUTION WHICH ASSURES WHITES A DISPROPORTIONATE SHARE OF POWER TO THEIR NUMBERS, HE REMARKED THAT IT HAD TAKEN THE UNTIED STATES FROM 1776 UNTIL 1964 BEFORE ALL AMERICAN BLACKS COULD VOTE.

"WHAT WE ARE SAYING IS THAT WE WILL NOT BE ARROGANT AND EXPECT OF OTHERS WHAT WE DID NOT DO OURSELVES," HE SAID.

IN THE ABSENCE OF ANY CONGRESSIONAL OBSERVERS HERE, THE FREEDOM HOUSE DELEGATION IS THE LEAST CONSERVATIVE AMERICAN MONITORING GROUP. SUSSMAN SAID ITS FINAL REPORT WOULD BE SENT TO CONGRESS AND PRESIDENT CARTER.

HE SAID THE INTERIM REPORT WAS BASED ON MORE THAN 600 INTERVIEWS WITH BLACKS AND VISITS TO MORE THAN 60 POLLING STATIONS.

SUSSMAN REFUSED TO SAY WHETHER HIS GROUP WOULD CALL FOR U.S. recognition of the new black-led government but this seemed to be the implication of the initial findings.

Meanwhile, the effort by nationalist guerrillas to disrupt the elections picked up, with Rhodesian military authorities reporting 10 landmine incidents over the past 24 hours. Six attacks on polling stations were recorded and four others on African groups going to the polls.

In one incident, three Africans were killed by a mine. In another incident at a polling station, a man was shot to death in a crossfire between guerrillas and security forces.

Since the general military mobilization for the elections April 12, 218 guerrillas, 12 members of the security forces and seven black paramilitary party auxillaries have been killed, the authorities said.

The government also announced that a woman waiting to vote and stepped out of line, given birth to a baby, gotten back into line and voted. It gave great publicity to a guerrilla who surrended yesterday and was taken to cast his vote in the elections. The guerrilla, recently trained in Ethiopia by Cubans, was quoted as saying "majority rule means that we are free. There is nothing left to fight for."

The government is counting heavily on a massive defection of guerrillas after the establishment of the government to reverse what has been a steadily deteriorating security situation.

Answering questions from observaters and reporters, Prime Minister Smith predicted "a big change" in the guerrillas' attitutde and an improvement in military affairs when the black government is installed.

Smith expressed concern that U.S. and British officials were setting loose a "few red herrings" to discredit the new constitution as another rationale for not recognizing the new government.

He said it was clear blacks would have 72 of the 100 seats in the new Parliament and whites only 28 and that blacks understood they were voting for black-majority rule.

The prime minister said Britain and the United States could not credibly argue over the number of seats reserved for the minority whites since in their own 1977 proposal they had set aside 20 for the whites as well as extensive guarantees for their rights.

Compared to other elections in Africa, where Smith said all but three countries were either under military dictatorships or one-party rule, Rhodesia's elections and constitution and come off very well, he declared.

Asked whether he was prepared to refuse a post as a minister in the new government to help improve its image aborad, Smith said he had repeatedly made concessions to the British and Americans only to be left "holding the bag" when they did not carry out their side of the bargain.

He hinted strongly that if Washington and London were ready to recognize the new black-led government, he would quit Rhodesian politics. But he said he would have to be certain of recognition.

"Let's make a plan that you will deliver the goods the same we do," he said in a reference to his resignation and Western recognition. "What could be more fair?" CAPTION: Picture 1, Rhodesian backers of Methodist Bishop Abel Muzorewa celebrate the voter turnout, dancing to a band in Salisbury. Muzorewa is favored for prime Minister. UPI; Picture 2, Women in Rhodesian village of Chirlonga wait to vote as guard stands by. UPI