President Reagan, speaking in translation live to the Soviet Union, appealed yesterday for a nuclear arms agreement and said that no other achievement could be more meaningful to him "as a husband, a father, a grandfather and as a person who loves God and whose heart yearns deeply for a better future."

The extraordinary address, broadcast from the Voice of America's studios here, explicity tried to dispel what Reagan called his "grim" image in some countries and to set the stage for his appearance Monday before the United Nations in which he is expected to present new arms control proposals.

Reagan's remarks were translated simultaneously for live broadcast in Russian and six other languages, including Ukrainian, Romanian, Lithuanian, Urdu, Bengali and Hausa. It will be translated into 34 other languages by the end of the weekend, VOA Director Kenneth Y. Tomlinson said, estimating the combined broadcasts will reach an audience of 100 million.

The administration kept word of Reagan's speech from the VOA a secret until Reagan went on the air in order to prevent Soviet jamming of the broadcast. The president's remarks were heard live in Moscow at 8 p.m. local time and were rebroadcast to the Soviet Union in English an hour later.

Reagan told his audience that his new proposals will continue to require the two superpowers to have equal arms strength and that only the "inflexibility of the Soviet government" on that point is preventing an accord. He said the United States has made five different proposals to reduce or "totally eliminate" nuclear arsenals only to be turned down by the Soviet leadership.

"I'm deeply aware of people's feelings and frustrations," Reagan said. "I share them. And I intend to keep trying.

"Yes, we insist on balanced agreements that protect our security, that provide greater stability and that are truly verifiable, but these requirements are the essence of fairness. They would provide greater security for all nations . . . the inflexibility of the Soviet government on arms control is holding back successful negotiations."

Senior White House officials said yesterday that the radio speech, which took the place of his regular weekly broadcast, is a preview of the U.N. address in which Reagan plans to couple a strong denunciation of the Soviet Union for downing the Korean Air Lines jet earlier this month with a new U.S. arms-reduction proposal.

"We deserve more support from the world," said one presidential adviser. "We don't shoot down airplanes or invade countries. We are making peace propsals while they massacre innocent people. We make reasonable arms proposals, and there is nary a move from the Russians. Where is the worldwide demand for them to compromise?"

In addition, White House officials said, the president will convey to U.N. delegates, as well as to U.S. Ambassador to the United Nations Jeane J. Kirkpatrick, that the United States wants to increase cooperation with non-aligned nations in order to win greater support for its stand in the arms talks.

In his speech yesterday Reagan referred to his image as a strong proponent of U.S. military strength as a possible cause for misconceptions about the U.S. stance in arms control talks.

"Now, I guess the picture painted of me by the officials in some countries is pretty grim," he said. "May I just say, and I speak not only as the president of the United States but also as a husband, a father, a grandfather and as a person who loves God and whose heart yearns deeply for a better future . . . . In this era of nuclear weapons, no achievement could be more meaningful than a verifiable agreement that would dramatically reduce the level of nuclear armaments."

Later, he appeared to be trying to persuade the Soviet people to question their government's claim that the South Korean jetliner was involved in espionage for the United States.

"I ask those who have been told the United States is reponsible: if you're hearing the truth, why has the outcry been so intense from members of the United Nations, the International Civil Aviation Organization, and why are pilots all over the world boycotting flights to Moscow? We have no quarrel with you, the Soviet people. But please understand that no government has the right to shoot civilian airliners out of the sky.

"Your airline, Aeroflot, has violated sensitive U.S. airspace scores of times, yet we would never fire on your planes and risk killing one of your friends or your loved ones," Reagan said.

Reagan spoke from the same VOA studio and used the same equipment used by President Eisenhower 25 years ago for a similar address to the world. Reagan has decried the VOA's outmoded equipment and promised to help modernize the government-operated radio station.