When House Democrats began drawing up a long-awaited bill to combat world terrorism, they received a rather frosty response from the Reagan administration.

Deputy Assistant Attorney General Victoria Toensing said the bill "would further hamper the already limited ability of the United States to extradite . . . fugitives." State Department legal adviser Abraham D. Sofaer said part of the bill "reads more like . . . a Pro-Terrorism Act of 1986."

Congress is slowly learning that cracking down on international terrorism, for all its political appeal, is a difficult legislative task. House and Senate lawmakers cannot even agree on how terrorist crimes should be defined.

"It is very easy for people to appear on TV and renounce, denounce and decry terrorism," Toensing said. Making "hard decisions," she said, is another matter.

One such decision is how to give the Justice Department "long-arm" jurisdiction to prosecute murders or assaults of U.S. citizens anywhere in the world.

U.S. law now covers foreign hijackings and kidnapings, but not murder. If Libyan agents murder an American in the Middle East, or if the United States captured the terrorists who bombed the Marine barracks in Beirut, the Justice Department still could not prosecute them for murder.

A bill sponsored by Rep. William J. Hughes (D-N.J.), chairman of the House Judiciary subcommittee on crime, would give the Justice Department jurisdiction over "crimes of violence" against U.S. citizens abroad. It says such crimes must be intended to intimidate or coerce a civilian population or government, and must be directed against the United States or a U.S. citizen.

But administration officials say this detailed definition would make it harder to prosecute terrorists by forcing the Justice Department to establish a defendant's motives and political purpose.

"Terrorism cannot be defined in any manner that is generally acceptable for a criminal statute," Sofaer told the subcommittee last month. For example, he asked, "Is a threat to blow up an airplane a crime of violence?" Would the recent killing of passengers at the Rome and Vienna airports be viewed as "directed against" the United States?

Sen. Arlen Specter (R-Pa.) has taken a different approach with a bill that has passed the Senate, 92 to 0. "We define terrorism without actually defining it," an aide to Specter said.

The Specter bill, which the administration supports, simply gives the Justice Department the power to prosecute any violent crime against U.S. citizens abroad, without spelling out the circumstances. The language is so broad that some fear it could be viewed as covering barroom brawls and muggings.

Specter tried to sharpen it by adding a "statement of findings and purpose," which says the bill is aimed at terrorism and that all such indictments must be approved by the attorney general. Any more precise definition, Specter's aide said, "becomes an element of the crime that the prosecutor has to prove in court."

But members of Hughes' subcommittee rejected this approach as granting too much discretion to the Justice Department. At the same time, the administration so vehemently criticized the rest of the panel's draft measure that Hughes quickly withdrew the other provisions.

One would have set standards under which the United States could extradite terrorists from abroad. The administration prefers to negotiate extradition procedures on a country-by-country basis, saying any worldwide definition of terrorist crimes must be reduced to the "lowest common denominator."

Toensing ripped into another provision that would exempt violent acts under the category of "political offenses." She told the panel that "murder, manslaughter, kidnapings, bombings and arson . . . could still be considered political offenses."

Toensing also criticized proposed standards for arresting and detaining accused terrorists, saying, "This bill makes it easier for those foreign fugitives to go on the lam again."

Hughes said he dropped the parts dealing with extradition, arrest and political offenses because "I feared it would sink the entire package." But his effort to produce a consensus bill soon foundered.

The subcommittee adopted an amendment by Rep. George W. Gekas (R-Pa.) that authorizes the death penalty for terrorist crimes covered in the bill. The amendment will be especially controversial because many U.S. allies do not allow capital punishment and the United States often promises to forgo the death penalty in making extradition requests.

"Having a death penalty in this bill is like shooting ourselves in the foot," an aide to Hughes said.