Poland has resumed making small interest payments on its debts to Western banks, raising hopes among nervous international bankers that a refinancing agreement can be completed to avoid default on more than $27 billion Poland owes to 460 banks and 16 countries in the West.

Default on the $17 billion owed to the banks, which could be touched off by the action of any one of them, would leave many banks in the United States and Western Europe with sizable losses. While they probably could be absorbed by American and British banks, according to industry analysts, such losses could be a heavy blow to the banking system of West Germany, Poland's largest lender.

U.S. and European taxpayers would cover some of the banks' losses, as well as the $10 billion Poland owes to their governments, if default is not staved off. The creditworthiness of the rest of Eastern Europe and the future of East-West trade also could depend, according to analysts, on how Poland's economy and finances emerge from the military crackdown ordered by Gen. Wojciech Jaruzelski.

The interest payments received by some of the banks during the past two days, according to Western European banking sources, were the first since martial law was imposed in Poland on Dec. 13. The sources said it was too early to tell whether the banks would receive all of the nearly $500 million they had demanded as a condition for rescheduling about $2.4 billion in debt, which Poland has been unable to pay in 1981.

"By the end of this week or early next week, the picture will be clearer," said one source. "But we have every reason to believe that Poland intends to honor its obligations."

A 19-bank task force handling the negotiations with Poland is continuing technical work on a refinancing agreement, which would stretch out repayment of Poland's 1981 debt over the next seven years at a slightly higher interest rate. More negotiations would then follow to determine how Poland would repay billions more falling due in 1982.

The 1981 refinancing agreement was scheduled to be signed today. But banking sources said it would have been delayed even if the Polish government had not cut off communications with the West when martial law was imposed.

The bankers' worries about completing the agreement were increased when the break in telex communications from Warsaw made it impossible for Polish banking officials to transfer money to make the required interest payments. These communications have now been partially restored, the sources said, and money has been trickling in from Polish funds on deposit in the West.

More money will be needed, however, if Poland is to pay all the interest demanded by the banks. A request by Poland for a $350 million bridging loan has been rejected, according to banking sources.

Western bankers are gambling that Poland will turn to other Eastern European countries and the Soviet Union instead, the sources said. They added that some bankers thought it would be wrong as well as financially unwise to extend Poland any more new credit than was absolutely necessary following the military crackdown.

Meanwhile, bankers in the Western task force have been trying to reassure the rest, to avoid a declaration of default by even a small bank on a relatively small debt that could quickly snowball into foreclosure by all 460 banks on the $17 billion Poland owes them. The bulk of that figure is uncovered by Western government guarantees.

Such a move would mean heavy losses for many of the banks, particularly those in West Germany who are owed a total of more than $4.5 billion by Poland, less than half of it covered by government guarantees.

American banks are the next most vulnerable. Poland owes them about $2 billion, about $800 million of which is covered by government guarantees or insurance. But banking officials, while remaining secretive about the exposure of individual banks, have said the American banking giants are comparatively much less vulnerable to a Polish default.

Highly profitable British banks also would be able to absorb a Polish default, according to industry analysts here.

Western governments already have rescheduled $2.6 billion of the $10 billion Poland owes them. They and the banks have been trying to buy time until Poland can join and borrow from the International Monetary Fund, a possibility also placed in doubt by the military crackdown.

The banks and governments remain dependent for repayment of their money on the success of Poland, however it emerges from the period of martial law, in reversing the rapid deterioration of the country's economy. Failure to meet its international financial obligations also could endanger the creditworthiness of the rest of Eastern Europe and the Soviet Union itself, according to analysts, making future trade and development more difficult.

This, in turn, further raises the stakes in the Polish crisis of Western European countries, particularly West Germany, which are deeply involved in trade with the Eastern Bloc. This and the risk to West German banks are among the reasons cited by European diplomats for the caution with which the West German government of Helmut Schmidt is responding to the crisis.

During the 1970s, when East-West detente was flowering, both Bonn and Washington were among the Western governments pushing banks to loan money to Poland. It had begun borrowing heavily from the West to finance imports of machinery, technology and grain to improve living standards and increase its industrial production. But mismanagement and bad harvests undermined these ambitious plans, according to analysts, and Poland failed to produce the increased exports needed to repay the loans.