The National Security Council and the office of Vice President George Bush shared responsibilities in setting up the elaborate anti-Sandinista supply system that came to light with the downing of an American-manned aircraft in Nicaragua last week, knowledgeable administration officials said Saturday.

The administration officials said that while the NSC recruited technical and logistical personnel retired from CIA or Army Special Forces in establishing the network, the vice president's staff concentrated on organizing Cuban exiles in Miami, many of whom were veterans of the CIA-organized Bay of Pigs invasion in 1961.

The officials said one of Bush's main contacts in Miami was his son Jeb, who is chairman of Dade County's Republican Party. None of the officials, however, provided specifics on Jeb Bush's involvement.

Spokesmen for the White House and the vice president's office on Saturday repeated denials that the U.S. government was involved in any way in efforts to provide military supplies to the anti-Sandinista rebels.

Reached at home in Miami Saturday, Jeb Bush also denied involvement. "Although I don't think there's anything wrong with it, I had nothing to do with it, " he said.

The role of the NSC and Lt. Col. Oliver North, the NSC's director of political development and political-military affairs, has been widely publicized in the past year.

But the contra connection to Vice President Bush, a former CIA director, had not been generally known, although it was first mentioned publicly in a little-noticed trial in Miami a year ago.

The October 1985 trial involved a private contra supporter, Jesus Garcia, who was charged with illegal possession of a weapon.

'BUSH'S BABY'

Garcia, questioned by Miami Assistant U.S. Attorney Jeffrey Feldman, said that an apparently bogus mission mentioned to him to blow up the Soviet and Cuban embassies in Managua was known as "George Bush's baby."

Garcia, in a telephone interview last summer, said a man identified as Alan Saum, who was the police informant against Garcia on the weapons charge, also had mentioned Bush's office as his contact point and left behind the White House telephone number and name of a "Col. Doug Menarcheck." A Lt. Col. E. Douglas Menarchik is one of Bush's military assistants.

Garcia said Saum was sent to Miami to entice him to join the fake embassy attack plan, but that in reality he was there to "put me in jail" because he had voiced opposition to other contra-related missions.

The contra link to Bush's office came to light when the only surviving crewman of the downed plane, Eugene Hasenfus, told reporters in Managua Thursday that a Cuban-American veteran of the Bay of Pigs named Max Gomez helped coordinate the intricate aerial supply system serving the contras from El Salvador.

ROLE OF ADVISER

Accounts published in several newspapers and wire services Saturday said Gomez told associates that he reported to Bush about his activities. The San Francisco Examiner said Friday that Bush's top adviser on the NSC, Donald Gregg, helped arrange the private contra supply network. Gregg is listed as Bush's assistant for national security affairs.

Bush, questioned during a campaign swing through South Carolina Saturday, described Gomez as "a patriot" whom he has met three times. But Bush did not comment on reports that Gomez reported to him on his effort to supply the contras. Bush's decision to avoid those reports followed a hurried strategy session among his aides Saturday morning.