President Carter formally proposed yesterday to set as ide a conflict-of-interest rule that would require his friend and confident, Budget Director Bert Lance, to sell a massive block of bank stock by the end of the year.

In a letter to the Senate Government Operations Committee chairman, Abraham Ribicoff (D-Conn.), Carter said that both Lance and the National Bank of Georgia, in which Lance holds more than 190,000 shares would suffer "an undue financial burden" if the deadline had to be met.

The price of the bank's stock has dropped sharply since Lance acquired it in 1975 and 1976. The bank reported this month that it was writing off $2.3 million in troublesome real estate loans in addition to $500,000 it had already checked off as bad loans earlier in the year.

The President said that Lance's commitment to sell his 21 per cent interest in the Atlanta bank, on top of its other problems, was contribution to "a substantial artificial lowering of the stock price."

Traded over the counter, NBG stock has been selling recently for $9 a share. Lance paid an average of more than $17 each for the 190,867 shares he had bought after going heavily into debt to raise the money. At the stock's present prices Lance would suffer a $1.6 million loss if he had to sell now.

Ribicoff had no immediate comment on the President's request. His Senate committee will consider it at a special hearing Friday morning Lance will be invited to testify.

The budget director's commitment to sell his NBG stock by Dec. 31, 1977, was first voiced following conversations with the President last November. Lance put the pledge in writing for the Government Operations Committee during confirmation hearings in January.

The President said yesterday that both he and Lance had " felt it highly desirable that Mr. Lance divest himself of his NBG stock, that he do so prudently and as soon as possible, but without significant financial hardship on his part." This, Carter indicated, is no longer possible.

Known as an aggressive investor who didn't hesitate to borrow money in order to make it, Lance, who used to be president ot the National Bank of Georgia, owes banks about $5 million altogether, according to a financial statement filed with the Senate committee in January. Last year, for instance, he borrowed $3.4 million from the First National Bank of Chicago and used part to pay off a $2.7 million loan he got in 1975 from New York's Manufacturers Hanover Trust Co. to help buy his National Bank of Georgia stock.

Carter noted that the stringent Dec. 31 deadline Lance had accepted was neither required by current federal law or by the administration's own conflict-of-interest guidelines applicable to other government officials.

Lifting the deadline, the President wrote Ribicoff, would simply mean that Lance would request designation of a new corporate trustee to dispose of "all the NBG stock in a prudent fashion without burden of a specific sale deadline."

The stock is now held by Dalton, Ga., businessman Thomas Mitchell, who holds Lance's other assets in a blind trust and who is currently operating under the injunction to sell the NBG stock by year's end and add the proceeds to the blind trust. Under the arrangement Carter proposed yesterday, the NBG stock will be turned over to a corporate trustee for disposal. Mitchell will remain in charge of the blind trust.

The President said Lance regards the proposed new arrangement as "desirable and acceptable" but feels it must have Ribicoff's approval since it is "inconsistent" with his earlier pledge.

A spokesman for Lance said last evening that the President acted "not in response to a direct request from Lance" but rather as the result of a letter he got several weeks ago from two NBG directors, Harold Brockery and John H.Stembler, who said they felt the deadline was unfair. The Los Angeles Times reported last Saturday, however, that Lance had told it on Friday that he was asking for the relaxation.

The bank will make its second-quarter financial report public today. It is expected to show a net loss, and reportedly may reduce or omit its 20-cent quarterly dividend.