The House Foreign Affairs Committee yesterday postponed action on a controversial bill to cut off funds for the administration's covert aid to Nicaraguan rebels after a testy partisan dispute over whether to debate the issue in public.

Democrats had voted in a caucus Tuesday night to close yesterday's meeting in hopes of moving the bill quickly to the floor. Republicans, however, said they would vote against a closed session.

If the debate were held in the open, "we could compromise sensitive information in the process," Rep. Stephen J. Solarz (D-N.Y.) said.

Rep. Henry J. Hyde (R-Ill.) countered, "I don't see anything to hide here."

The partisan split left the committee in confusion in the morning session. In the afternoon, after conferring with House Democratic leaders, Chairman Clement J. Zablocki (D-Wis.) announced that both sides had agreed to consider all amendments to the bill yesterday, first in a closed session, and then in open session with 20 minutes allotted to each side for the public debate.

The dispute, while on a procedural matter, illustrated the extent to which Central America has become a partisan issue in Congress. Democrats want to score points against the administration, but are anxious to avoid blame if more of Central America comes under leftist control. Republicans want to paint Democrats as soft on Marxism.

"As Central America becomes an issue in the national presidential campaign, it is important for the Democratic Party to take a position," said Rep. Peter H. Kostmayer (D-Pa.) "The longer this issue is dragged out the less decisive impression there is in the country that the Democrats have taken a clear-cut stand."

Kostmayer added, "The real reason the Republicans want an open session is politics. They want to embarrass the Democrats."

However, Rep. William S. Broomfield (R-Mich.) called the Democratic argument that classified material might be divulged "a bunch of hogwash."

Democrats said they feared that the Republicans would be able to slow down and water down the Zablocki-Boland bill, which would cut off funds for CIA support to some 7,000 counterrevolutionaries battling the Sandinista government.

It would replace the covert aid with an open program of $30 million this year and $50 million in 1984 to friendly Central American countries to be used to interdict arms flowing from Nicaragua to guerrillas in El Salvador.

Republicans prepared several amendments to the bill, including one sponsored by Broomfield which would allow the covert program if the president certifies that it is necessary to deter arms shipments and for further negotiations.

Rep. Edwin V.W. Zschau (R-Calif.) said that the increase in open funding for arms interdiction might require additional U.S. advisers in Central America, and "that issue should be debated openly."

Hyde said the $80 million arms interdiction program "is called cover my posterior: if Central America falls, they the Democrats want to be able to say we did something."

Democrats, however, said the money is necessary for conservative Democrats to support the bill on the floor.

Few people think the bill as written will become law. The Senate has enacted a different version, which allows the covert funds to be released if the intelligence committees of both houses approve. In any event, the president is considered likely to veto the final bill.