A blue-ribbon presidential panel began work yesterday on one of the nation's most serious and politically sensitive problems: how to prevent bankruptcy for the giant Social Security system, the main source of income for three-fifths of the nation's elderly.

Alan Greenspan, former chairman of the Council of Economic Advisers, whom President Reagan named to head the 15-member National Commission on Social Security Reform, opened the panel's first meeting on a conciliatory note. He read a letter from the president declaring that "every American of every age has an important stake in your work."

Last year the president proposed deep short-range and long-range cuts in Social Security, which will pay more than $200 billion in benefits next year, and ruled out any increase in the Social Security tax or infusion of general treasury revenues to avoid such cuts.

At that time Democrats, led by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), said the cuts were far more than needed to put the system on a sound footing and were an attempt to balance the federal budget on the backs of Social Security recipients.

Public hostility to the president's proposals was so great that he withdrew them and named the panel to try to work out a bipartisan solution.

Greenspan, in an attempt to get deliberations off to a good start, tendered the olive branch toward Democratic members of the commission, such as AFL-CIO President Lane Kirkland, former Social Security commissioner Robert Ball, Rep. Claude Pepper (D-Fla.) and Sen. Daniel Patrick Moynihan (D-N.Y.), who have been highly critical of the president.

He bent over backward to show procedural fairness and quickly disposed of issues that could have divided the commission: whether members who favor strengthening the system by pumping in general revenues from the treasury, instead of cutting benefits, would be permitted to offer proposals to that effect, and whether those who dissent from the final report, to be filed by Dec. 31, will be able to file minority reports.

"We must clear up whether certain steps are precluded, such as general revenue financing," said Kirkland.

"We are fully free and unshackled," said Greenspan. He added, "The final report will be by majority votes and we will also record dissenting opinions."

At Moynihan's request, Greenspan called on the current Social Security commissioner, Jack Svahn, to make clear whether Reagan would take a look at all the commission's recommendations or would only consider cuts. "The president has said the commission should be open to all options," said Svahn, adding that a wire service story suggesting Svahn had said otherwise was a misinterpretation.

Robert J. Myers, former chief actuary and deputy commissioner of Social Security and now executive director of the national commission, then sketched out the system's basic problems:

The old-age fund, the largest of the three trust funds, will be unable to meet all benefit payments sometime late this year because "in the 1970s economic conditions just went haywire," with much greater inflation and higher unemployment than anticipated, producing greater outlays and less income.

With borrowing from the better-off disability and Medicare trust funds, which Congress has already authorized, the old-age fund can get by until mid-1983. If added borrowing were allowed, the fund could perhaps get by a few years more if the economy picks up substantially, but the margin of safety would be thin. If it failed to pick up, the fund would run short.

The situation will improve as new taxes already voted in 1977 kick in during the late 1980s and produce more revenue.

But 10 or 20 years into the next century, if current projections prove correct, there will be severe financial shortfalls.