House-Senate conferees agreed yesterday to restore for 3 million current recipients the $122-a-month minimum Social Security benefit Congress voted to repeal earlier this year in one of President Reagan's budget cuts.

The conferees also approved stopgap borrowing to keep the Social Security retirement system from going broke during 1982, leaving the question of long-term financing reform to later.

The House and Senate are expected to act on the conference agreement later this week before adjourning for the year.

The agreement would allow no new retirees to qualify for the minimum benefit after Dec. 31, except nuns and other members of religious orders who have taken vows of poverty. The Democratic House had proposed restoration of the benefit for all future retirees, and a fight to include them is expected when the House takes up the measure.

The Dec. 31 cutoff date gives a reprieve to an estimated 4,400 retirees who would have become eligible for the minimum benefit in November and December under the laws that stood before this year. Under the budget "reconciliation" bill that Congress passed last summer, the minimum benefit rolls were supposed to have been closed as of last month.

The minimum benefit goes to those whose Social Security contributions would otherwise qualify them for less. It establishes a floor for benefits no matter how little a person has worked, nor for how little pay.

It was the only major benefit cut Congress approved last summer. Reagan proposed others but backed off when Democrats began portraying him as opposed to the program, which helps support one in seven. His retreat has left the long-term future of the program in limbo.

To offset most of the cost of restoring the minimum benefit, the conferees agreed to tax sick leave by considering the first six months of such compensation as taxable income. This would cover all but $1.7 billion of the estimated $6.1 billion cost of restoring the benefit over the next five years.

But the conference dropped Senate proposals to reduce the minimum benefit for people receiving local, state or federal government pensions of more than $300 a month and to impose a maximum family benefit under the retirement and survivors system.

The agreement to let the nearly depleted retirement system borrow from the better-off hospital and disability insurance funds through Dec. 31, 1982, was intended to keep the retirement system solvent until a more comprehensive retirement financing solution is found next year.

As a whole, "it was the best compromise we could reach," said Rep. J. J. (Jake) Pickle (D-Tex.), chairman of the Ways and Means subcommittee on Social Security. "It shows compassion for the minimum benefit recipients. It shows determination to tackle the overall problem of financing in the earliest possible time."

House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) said, "While the conference agreement does not achieve all our objectives, it constitutes a major victory with regard to our No. 1 concern: the protection of minimum benefits for those now receiving them. It represents a first step in making good on President Reagan's own campaign commitment to protect Social Security benefits."