The comments were made after Thatcher became leader of the Conservatives in February 1975, when the party was still in opposition.
Thatcher became prime minister when the Conservatives won the May 1979 elections.
The once-secret files released on December 29 to Britain's National Archives after 30 years showed that Foreign Office officials thought she should break off ties with local Jewish groups.
They also suggested Thatcher should swap her parliamentary constituency of Finchley in north London - which had a large Jewish population - for one deemed more acceptable by Arabs.
Thatcher's membership of groups such as Conservative Friends of Israel and the Anglo-Israel Friendship League of Finchley was raised during a visit to Jordan by Conservative foreign affairs spokesman Lord Carrington in 1975.
Michael Tait, an official at the British embassy at the time, noted: "He asked the ambassador's advice on this and was assured that such a connection, which would inevitably do much harm in the Arab world, should if at all practicable be severed.
"Carrington agreed that Mrs. Thatcher might most painlessly and with some justification get herself off the hook by resigning from all constituency obligations of this sort on the grounds of the rather wider obligations she has now to assume.
"Such a stratagem might resolve the problem in Finchley but if Mrs. Thatcher is indeed a prime mover in a wider parliamentary grouping of pro-Israeli MPs then the difficulty would be trickier to bypass.
"While we as government and not opposition officials may have no particular brief on Mrs. Thatcher's behalf it is presumably in the national interest to do what we can to counter Arab fears and suspicions that the leader of HM [Her Majesty Queen Elizabeth II's] opposition is already a prisoner of the Zionists."
In a handwritten addition, Tait asked: "Why don't you advise her to swap Finchley for Westminster?" another safe Conservative London constituency seat.
The Foreign Office was also sympathetic, noting that the Conservative Party was "well aware of the problems which these links might pose".
One official added however: "We do not think there is anything we can, or should, do about Mrs. Thatcher's membership of pro-Israeli organizations."
Thatcher was the president of the Anglo-Israel Friendship League of Finchley in 1983 and was still president of Finchley Friends of Israel in 1990, having helped found it in 1963.
© 2005 Agence France-Presse
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