Poland has paid small amounts of interest on its 1981 debt to western banks in the last two weeks and has assured financiers that it will pay the balance of the back interest by the middle of February, U.S. and European banking sources reported yesterday.

In the weeks since martial law was imposed in Poland, its international debt has emerged as a major political and economic problem for the military government.

Western governments and commercial banks have informed Polish authorities that they will not even discuss new loans or aid until the interest owed to the commercial banks from 1981 is paid.

Poland's inability to keep up with the interest payments has also made the regime vulnerable to a formal western announcement of default that could destroy the country's credit rating. Some hard-liners in the United States have been urging the Reagan administration to take a tough position under which the Poles would have to go to the Soviets for the money they owe or face default.

Two senior banking sources in New York said yesterday that money has come from Poland recently. One large international bank, Morgan Guaranty, is reported to have only several hundred thousand dollars in interest still outstanding from 1981.

Meanwhile, Polish authorities advised the Union Bank of Switzerland by telex Thursday that they intend to complete paying 1981 interest by the middle of February, according to banking sources in Frankfurt quoted by the Reuter news agency.

This would clear the books for 1981 and set the stage for a new round of talks between Poland and the western bankers about debt coming due this year.

However, bankers say there are still major questions about Poland's ability to make good on its promise. Some estimates of the 1981 interest still owed run as high as $200 million. Analysts say it is doubtful that Poland will earn enough from exports between now and Feb. 15 to cover that amount, and it is unclear whether the Soviet Union will help.

"It's not that there's another shoe that still has to drop," said a western banking official. "It's that we're living under a shoe store."

West European publications reported this week, for example, that a $23.7 million Polish government bond redeemable Jan. 13 had not been paid off. One source said that western bankers who are owed money from 1981 were incensed when the Warsaw government redeemed bonds that had come due earlier. They argued that the bond buyers, most of whom are thought to be other banks and big investors, should be exposed to the same risks as other creditors.

Private banks in western industrial countries are one group of creditors. They are owed about $7.4 billion, with West German and American banks in the lead.

In addition, Poland owes $13 billion to foreign governments, and $6 billion to Soviet, East European, South American and Arabic banks.

Poland's financial negotiations with the private western banks have been separate from talks with the creditor governments.

At this point private bankers prefer to take a wait-and-see attitude, hoping that Poland can come up with the money. But U.S. banks are facing immediate pressure from their accountants to decide how to carry these loans on their books. These decisions will have an effect on annual profit-and-loss statements, now in preparation, and will figure in the way stockholders evaluate bank managements.

One bank, Marine Midland, has indicated that it will set aside a reserve out of profits to offset a potential loss on the Polish loan. If the loans go unpaid indefinitely, U.S. bank regulators could step in and insist that all the banks make provision for losses on Polish loans.