Federal Roads Commissioner Lowell K. Bridwell met behind closed doors with the City Council and their academic advisory committee on the Inner Belt for two and a half hours yesterday to discuss the fate of the highway.

Bridwell reportedly termed the advisory committee's proposal for a two year, $5 million re-study of the highway "conceptually excellent," but doubted than such a study of the long-range social costs of a highway was feasible at present. He presented a more limited counter proposal, which emphasize finding ways for Cambridge to cope with the Belt, rather than exploring various alternatives to it.

The commissioner did concede, however, than eliminating the Belt altogether should be considered. All metropolitan transportation plans since 1948 have assumed that the Belt--in some form--would be built.

Councillor Daniel J. Hayes Jr., who is heading the City's fight against the Belt, expressed guarded optimism after the meeting. "I won't say he (Bridwell) has frozen his position--he's open," Hayes said. But the councillor had two objections to the commissioner's counter-proposal:

* The money for the study would go to the state, not to the City. The Massachusetts Department of Public Works (DPW) has long suported the Belt.

* The study would be made using "existing data and techniques"--assumption which the City feels prejudge the case in favor of the highway.

Thursday morning, the council will "sit down" with Bridwell, the DPW, and representatives of the Department of Housing and Urban Development in Washington to try to iron out a compromise plan for a Belt study. According to usually reliable sources, Bridwell might then announce a decision to build the Belt if a compromise is not reached.