Antiterrorism Act of 1986 - Amends the Federal criminal code to establish a new Federal offense of international terrorism. Defines international terrorism as an act of violence directed against the United States or a national of the United States which is intended to coerce, intimidate, or retaliate against a government or civilian population. Establishes criteria for the imposition of the death penalty where a death results from an act of international terrorism. Lists mitigating factors (including the defendant's age and mental capacity) and aggravating factors (including previous convictions and the nature of the offense) for jury, or court, consideration. Requires the government to serve notice upon the defendant a reasonable time before trial or acceptance of a plea that it intends to seek the death penalty and the aggravating factors upon which it will rely. Requires a separate sentencing hearing to determine the punishment to be imposed upon a defendant found guilty of international terrorism. Requires the court, or the jury by unanimous vote, to impose the death penalty upon a finding that such sentence is justified based on consideration of both the mitigating and aggravating factors. Requires the court to instruct the jury not to consider the race, color, national origin, creed, or sex of the defendant when sentencing. Establishes procedures for the appeal of a death sentence. Requires the court of appeals, upon consideration of the trial record, information submitted during the sentencing hearing, and the procedures of such hearing, to affirm the decision if: (1) the sentence was not imposed under the influence of passion, prejudice, or arbitrariness; and (2) the information supports the finding. Requires the court to provide a written explanation of its determination. Establishes procedures for the implementation of the death penalty. States that the death penalty shall not be carried out upon pregnant women. Requests the President to study the threat of terrorist attack and means to control the availability of and use of explosives by terrorists. Requests the President to report the results of such study to the Congress. Expresses the sense of the Congress that the President should establish a process to encourage the negotiation of an international convention to prevent international terrorism. Amends the Omnibus Crime Control and Safe Streets Act of 1968 to provide assistance in developing and implementing antiterrorism plans for deep draft ports, international airports, and other important facilities. Makes the transmission of threats in foreign commerce, as well as interstate commerce, a Federal offense.