Former National Security Advisor Zbigniew Brzezinski last night urged Republican and Democratic leaders to improve the conduct of American foreign affairs over the next few years by working together to achieve common goals and by publicly downplaying political differences.

In an address to 500 gathered at the Kennedy School's Institute of Politics Forum, Brzezinski called for a return to "substantive bipartisanship" and for measures which he said would make possible "more serious, searching, and responsible discussion" of foreign policy issues than has taken place recently.

Urging Presidents to stress "continuity, not contrasts" between Administrations and to focus on the long-term interests of the United States, Brzezinski proposed a return to "relationships of personal trust and personal involvement" between Presidents and selected Senators.

Brzezinski, who served under President Jimmy Carter, also suggested that Cabinet members hold monthly bipartisan meetings with legislators to discuss foreign policy, that Administrations create more bipartisan commissions, and that the President widen his circle of foreign policy advisors.

He called such measures "essential" for reviving "shared consensus at home," and said Presidents should make a "systematic and determined effort" to get them implemented.

Brzezinski, who returned in 1980 to his teaching post at Columbia University, engineered the aborted rescue of Iranian hostages and was instrumental in forcing out then-Secretary of State Cyrus Vance. He taught at Harvard for seven years during the 1950s.

Brzezinski assailed both of the Presidential candidates' defense programs, calling "unsophisticated" Walter F. Mondale's support for a nuclear freeze and terming President Reagan's "Star Wars" defense scheme unrealistic. Mondale takes arms control and "elevates it to a fetish," he added.

He called instead for some form of defensive weaponry to enhance the country's security, and a foreign policy based on strength and arms control.