President Carter, dodging questions about the political threat posed to him by Sen. Edward M. Kennedy, used the backdrop of Kennedy's home region of New England today to ask the nations oil companies to freeze home heating oil prices this winter.

The president pledged that the nation will not run short of fuel during the winter heating season and said he has asked other oil companies to follow the example of Texaco, which last week announced it planned to hold home heating oil prices at their current level, already a record high, and ease credit requirements to consumers during the winter.

"I'm asking the other 27 major oil companies to act in a similarly responsible manner to freeze prices and give adequate credit to help us through this winter with heating oil," Carter said.

Carter made it clear one subject he did not want to discuss was Kennedy, who for the first time has said publicly he may challenge Carter for the Democratic presidential nomination. At the airport in Pittsburgh, where he stopped on the way to an "energy town meeting" in nearby Steubenville, Ohio, a reporter asked the president who he thinks would win a race between him and the Massachusetts senator.

"Nice day, isn't it?" carter replied.

"You don't want to talk about it, sir?" the reporter inquired.

"How did you ever guess that?" Carter said.

Carter initially made the request for a price freeze Saturday in telegrams to oil company executives, asking companies to take actions similar to Texaco's "to help keep heating oil prices stable and to assist in meeting emergency supply and credit needs."

The White House made a routine announcement of the request, which attracted little public notice. But today, in a speech to the National Retired Teachers Association and the American Association of Retired People, the president repeated the request, specifically calling for a freeze on home heating oil prices.

White House press secretary Jody Powell said later there has been no response thus far from the oil indus- try. He declined to discuss what the administration would do if the request is turned down.

Home heating oil prices are already 50 percent higher than last year. According to the Department of Energy, the average price of heating oil has risen from about 43.7 cents a gallon in January to well over 80 cents.

Nowhere is the price and availability of heating oil a more politically explosive issue than in New England, where between 60 and 70 percent of the households use heating oil. Thus, while the two organizations he addressed were meeting here on health care issues, Carter's main theme was energy.

The president announced the details of legislation, sent to Congress today, to provide $1.6 billion in federal funds to the poor to help pay higher fuel costs this winter. The legislation calls for the assistance to increase to $2.4 billion in later years.

Of the initial $1.6 billion, $1.2 billion is dependent on passage of the administration's proposed "windfall profits" tax on the oil industry. However, a White House official traveling with Carter suggested today that if the tax proposal is not enacted by Congress this year, the administration would be willing initially to use general revenue funds for the assistance program.

The president also announced that later this month the government will establish an energy "management team" in Boston to monitor the delivery of home heating fuel supplies to New England, which he predicted will be sufficient for the winter.

Administration officials said that under the assistance legislation introduced in Congress today, the average payments this winter would be $100 for individuals and about $200 for families. They estimated that 7.3 million households would benefit from the program.

According to administration figures, the average payments in the District of Columbia the first year would be $97.16 to poor individuals living alone and $194.32 to families. The comparable figures in Maryland would be $103.45 to individuals and $206.93 to families, and in Virginia would be $97.91 to individuals and $195.41 to families.

The payments in the first year of the proposed program would go only to individuals or families receiving Aid to Families with Dependent Children or payments under the Supplemental Security Income program. In later years, individuals or families with incomes of less than 125 percent of the federally determined poverty level would be eligible.

After his speech in Hartford, Carter took questions from his elderly audience -- the first of which was why he favors phasing in national health insurance, rather than attempting to enact a complete health insurance plan at once, as is advocated by Kennedy.

Carter gave his usual reply -- that his approach can get through Congress, while Kennedy's cannot. And in answer to several other questions about health insurance, he repeatedly stressed the similarities between his plan and Kennedy's and his willingness to work with his potential rival on the issue.

While the president steadfastly ignored it, Kennedy's name swirled about him throughout the day. At the Hartford airport, Connecticut Gov. Ella T. Grasso said of a potential Kennedy candidacy, "If Teddy is a candidate, he will be tremendously popular in Connecticut."

But Grasso, who has endorsed Carter for renomination and reelection, said she is sticking with her earlier commitment and stressed the importance of loyalty in politics.

Another Connecticut politician, Republican Sen. Lowell P. Weicker Jr., was even blunter in his assessment. Kennedy would win a confrontation with Carter "in a landslide," Weicker said, adding that "every Republican senator" hopes Democratic tickets across the country will be headed by the president, not by Kennedy, in 1980.

Weicker's remarks clearly miffed press secretary Powell, particularly because they were made while Weicker was Carter's guest aboard Air Force One.

"I always thought that anybody that was born that rich would also have been brought up with some manners," Powell said of Weicker.

While the Kennedy-Carter rivalry was the chief topic of interest among reporters and politicians traveling with the president, there was little evidence of it among the voters. In Steubenville, a large, friendly crowd lined the streets to greet Carter. At least one "draft Kennedy" sign was held aloft, but farther down the street another spectator countered with a "Jimmy not Teddy" sign.