A House subcommittee issued subpoenas yesterday for records of accounts in 13 banks, most of them in Florida, in order to trace mysterious paths taken by some of the $27 million in nonlethal aid that Congress approved last year for rebels in Nicaragua.

Rep. Michael D. Barnes (D-Md.), chairman of the Foreign Affairs subcommittee on Western Hemisphere affairs, said the subpoenas he signed were a last-resort effort to "provide the missing paper link" proving that the rebels, known as counterrevolutionaries or contras, actually received the amount and kind of goods authorized.

The action followed testimony from a General Accounting Office official that the final destination of $13.3 million cannot be verified with available records and existing procedures. Barnes has said the GAO expects the unverifiable spending to total about $15 million.

The names of banks affected are classified, but one is known to be here, one in Chicago, one in Hialeah, Fla., and the rest in Miami.

Barnes said the 16 accounts belong to brokers who received deposits from the Nicaraguan Humanitarian Assistance Office, which runs the aid program, and to individuals and suppliers of goods. Some former contras say that "skimming operations" use false receipts and cash transfers to divert the funds.

The full committee voted, 24 to 0, to allow Barnes to sign the subpoenas after the subcommittee approved them, 9 to 0.

Ranking minority member Robert J. Lagomarsino (Calif.) said Republicans joined in the vote because "we don't want to be perceived as covering things up" and because "damaging information" was not likely to emerge.

Bosco Matamoros, spokesman for the largest rebel group, the Nicaraguan Democratic Force (FDN), said it "welcomes this inquiry because the debate should not be based on allegations."

He added: "We hope this is not a political effort to paralyze U.S. support for democratization in Nicaragua."

A State Department spokesman said Barnes' panel "is trying to make a political issue out of this. What they're really going to find is that the inadequacies that exist in the system are the ones that Congress wrote into it. They're trying to shift the blame."

The Reagan administration has been fighting for congressional approval of $100 million in covert military and "humanitarian" aid to the contras, arguing that the existing overt program is all but impossible to administer and is inadequate to pressure Nicaragua into political reform.