Months of campaigning and millions of dollars behind his rivals and ignoring the advice of friends and family, George McGovern yesterday stepped back into what he called "that great forum" of running for president with a call for peaceful coexistence with the Soviet Union and other communist countries.

Speaking to a friendly crowd of several hundred students and well-wishers at George Washington University, the low-key "prairie populist," 61, launched another try for the presidency on the same liberal and anti-war themes that swept him to the Democratic nomination in 1972, only to be devastated in the worst defeat in American presidential history.

"The system of war as a means of settling international conflict is now obsolete," he said in a 25-minute address that emphasized the need for arms control, an end to U.S. military involvement in Central America and improved relations with Cuba.

"I would not be seeking the presidency a second time if I did not believe with all my heart and soul that I have the God-given capacity to lead this great nation away from the abyss into the ways that make for peace," he said.

"I am speaking about hard-headed negotiations with the tough-minded leaders of the Soviet Union. I am speaking about having the informed judgment to end our deepening military involvement in Central America. I am speaking about having the sense of justice and prudence to tell the warring parties of the Middle East that there will be no more American aid and no more American soldiers unless Arabs and Israelis and Palestinians get to the conference table . . . . "

Regarding the Sept. 1 Soviet shooting down of a South Korean jetliner, he said the act was "outrageous" and "underscores the folly of the present Cold War tension . . . . "

Although he said he would speak on these issues with a sharper edge than the other Democratic candidates will, he said he was running not against them but against President Reagan.

The new candidate was flanked by his wife, Eleanor, and other family members and loyalists, but many made it plain that they were there as friends and not as campaigners. Many of his former supporters and liberal Democrats have made it known that they consider his entry potentially harmful to the party as well as to himself, and that he still carries the heavy baggage of an image as a fuzzy-headed liberal.

Eleanor McGovern said that she does not intend to campaign for her husband and that she and some of their five children had been concerned about how he might fare.

"We just hate him to take the risk of being hurt again," she said.

But she added that she is "proud of his reasons for wanting to run" and may change her mind about campaigning later.

McGovern praised his wife's independence, and was applauded when he said, "I and other politicians have to get over the notion that we can just throw our wives into political combat."

Sen. Gary Hart (D-Colo.), who managed McGovern's 1972 race, is one of the six other announced Democratic candidates, and George Cunningham, a McGovern aide for three decades, said he is busy thinking about his own possible Senate campaign in South Dakota and will not be available.

"I have always respected George McGovern's views and commitment to peace and I think he can offer a contribution to the debate," Hart said.

When consulted by his former boss, Cunningham said, "I played devil's advocate pretty strongly, mentioned the possibility he might be savaged by the press, the cartoonists, mentioned the possibility of the Harold Stassen imagery . . . . " Cunningham agreed with speculation that McGovern might be motivated in part by the feeling of being out of the action since his defeat in his 1980 Senate race.

"You know, you're in it that long and suddenly the phones don't ring. But that alone is not enough to make somebody run for president . . . . I think he's going in with the bark off and the hide showing, without a specific political constituency, trying to see if he can marshal one," Cunningham said.

On Capitol Hill, Sen. Christopher J. Dodd (D-Conn.) called McGovern's decision "ill-advised," and said his presence in the Democratic field could hurt the party's attempts to appeal to a broader constituency.

In a news conference after his speech, McGovern shrugged off questions about his lack of money, organization and apparent constituency with the argument that it is the candidate and his ideas that count.

"Don't worry," said the man who had been spotted at a copy shop running off copies of his own announcement speech the day before. "The importance of a campaign manager is overestimated anyway."

McGovern denied he has been "Stassenized," referring to the hopeless campaigns of Harold Stassen (a candidate again), saying his first run in 1968 was only as an 11th-hour stand-in for the assassinated Robert F. Kennedy.

Since he lost his 1980 bid for a fourth Senate term, McGovern has been lecturing and writing, and founded a liberal political lobbying group called Americans for Common Sense, whose Connecticut offices are metamorphosing into his campaign headquarters. Since coming to Washington in 1956 he has accumulated a modest personal fortune through real estate investments and lecture fees.