A New Jersey woman pleaded guilty in federal court here yesterday to conspiring to violate the Arms Export Act as part of a scheme to ship sophisticated electronic navigational tracking equipment to Syria, a deal that she admitted involved a former embassy official here.

Rosemary L. Loughery, 42, of Mount Holly said in court that she agreed with the prosecutors' written statement of evidence against her in which Souha Jamali, formerly the third secretary at the Syrian Embassy here, was identified as the local contact for Loughery's business associate, Kevin P. Gilday.

Jamali left the United States in November, several days after Loughery and Gilday were arrested. The Syrian Embassy has denied that Jamali was involved in any arms deals, insisting that her frequent contacts with Gilday concerned oil deals.

Embassy officials have said Jamali was recalled to Damascus after staff cutbacks here that were ordered as part of American sanctions against Syria. President Reagan announced the sanctions Nov. 14 to show U.S. "outrage" at Syria's involvement in international terrorism, including the bombing of a nightclub in West Berlin in which two persons, including an American serviceman, were killed.

Loughery and Gilday had been charged in a 10-count indictment that also alleged the two had been negotiating to provide C130 transport planes to Libyan leader Moammar Gadhafi and military hardware to Iran. The hardware, according to court documents, included TOW, Dragon and Stinger battlefield missiles and spare parts for tanks, helicopters and F4 and F5 aircraft.

No equipment was shipped out of the United States.

During yesterday's hearing, U.S. District Judge Thomas P. Jackson set a Nov. 30 trial date for Gilday, who remains under house arrest at his parents' home near Wilmington, Del. Loughery is free under a cash bond.

Assistant U.S. Attorney Mark Biros said Loughery could be sentenced to five years in prison and fined $250,000. Jackson set sentencing for Sept. 11.

The two were arrested after a year-long undercover investigation by U.S. Customs agents posing as American arms dealers who could deliver military hardware and computer systems to Gilday. The agents, Donald Bludworth and Robert Fischer, knew Gilday "as a person who previously had been involved in efforts to transship illegally high-tech equipment through Europe and the Middle East to the Soviet Union and Eastern Bloc countries," according to the evidence statement.

Gilday and Loughery were working with Thomas O'Brien, who, authorities say, has ties to the Irish government, the Irish Republican Army and English arms trader Eric Magee, the statement said.

According to court documents, Syria wanted to buy 20 tactical and 20 semi-fixed radio navigational beacons manufactured by Gould Electronics in California. Sale of the equipment to Eastern bloc and most Middle Eastern countries is illegal.

Magee was working directly with the Syrian government, and O'Brien was to provide "end use country" certificates that would show the beacons were going to Cyprus instead of Syria, according to the written evidence statement.