The State Department expressed growing concern yesterday about the "cycle of terrorism, repression and protest developing in Chile." But the administration also voted for a $125 million loan to Chile from the Inter-American Development Bank despite calls for the United States to oppose the loan to protest President Augusto Pinochet's repressive tactics.

These moves came as the Chilean military government deployed thousands of troops to put down protests called by opposition leaders demanding a swift return to democracy.

State Department spokesman John Hughes, echoing earlier statements of U.S. concern, said the clashes in Chile are impeding efforts to restore democracy and added: "Clearly some initiative is needed to break this impasse."

At the same time, however, U.S. representatives to the IADB, where the United States has 35 percent of the voting rights, voted to grant the loan to help municipal investment in Chile. Last week, the United States, which is the largest contributor of IADB funds, voted for a loan of $35.7 million to Chile.

These actions were taken despite appeals from congressional liberals that the administration seek to send Pinochet a signal of disapproval by returning to the Carter administration policy of opposing, for human-rights reasons, all so-called "nonbasic human-needs loans" to Chile. The Reagan administration abandoned that policy in 1981.

A senior State Department official, who declined to be identified, denied last night that the U.S. actions were inconsistent. He said the United States supported the latest loan on grounds that it was "economically justified in terms of meeting the obvious need of Chilean people for assistance."