A spokesman for House Democrats asked President Reagan yesterday to respond to allegations of illegal activity by the Nicaraguan contras and some of their American backers before the House votes again on giving the contras more money.

"In the last 48 hours, new allegations have surfaced that the contras are involved in illegal gun-running and are financing their operations with the sale of cocaine," Rep. Mel Levine (Calif.) said in the Democrats' weekly radio address.

On Friday The Associated Press reported that federal officials, including the Federal Bureau of Investigation and the U.S. attorney for southern Florida, were investigating charges that the counterrevolutionaries have engaged in drug trafficking to finance their battles with the Nicaraguan government and that possibly illegal arms shipments have reached neighboring Honduras and Costa Rica from the United States.

Levine, chairman of the House Democratic Caucus task force on Central America, said that if the president does not provide a written report on these allegations, "it would be inappropriate for Congress to give the contras one penny in additional aid."

The House, which has rejected the president's $100 million aid request, is expected to take up the Senate-passed proposal again Tuesday.

A White House spokesman declined to comment yesterday on Levine's call for a written report from the president. Peter Roussel, deputy press secretary, said, "The president's position on contra aid is well known."

In addition to the allegations of drugs and arms, the aid proposal is caught up in a procedural dispute involving House Democratic leadership plans to attach it to the fiscal 1986 supplemental appropriations bill.

The Reagan administration is adamantly opposed to sections of the spending bill and has threatened to veto the measure, even if it includes contra aid. The administration has been trying to persuade House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) to keep contra aid separate.

Levine's call was voiced in the Democrats' response to the president's weekly radio address. Reagan, however, did not talk about contra aid but accused Congress of dragging its feet in the budget process.

Assailing Senate consideration of a tax increase and House consideration of increased domestic spending, Reagan asked, "Isn't it time the Congress got government out of the way -- and let the good times roll?" As for any tax increase, he declared: "My veto pen is inked up and ready to go."

Reagan's attack on Congress followed last week's vote by the Republican-controlled Senate against taking up his tax overhaul proposal before he reaches a budget compromise with Congress.

The 72-to-24 vote reflected growing anger at the administration and a belief that the budget stalemate results from Reagan's unwillingess to bargain, not congressional intransigence.

White House officials reportedly rejected using yesterday's radio speech to discuss contra aid because they want to continue negotiations with O'Neill and do not want to intensify the partisan conflict on the issue.