Local government minister Hilary Armstrong announced last week that councils are to gain the power to promote the economic, social and environmental well-being of their areas.
The move - promised in Labour's general election manifesto - comes after two years of campaigning by the Local Government Association and was this week reaffirmed by environment minister Lord Whitty.
But ministers are facing growing pressure to flesh out the pledge and say how they will introduce the new power, which is similar to a duty already planned for the new London assembly.
In a special Lords' debate on council roles, he said: 'Now is the time for the inclusion of this duty.'
Lord Bassam said the move would send out a clear message about the role of local government.
It would 'enshrine in law local authorities' role as the elected leaders of the local community, with a responsibility for the well-being . . . of their area'.
The call to include the new duty in the draft Bill was also backed by cross-bench peer Lord Hunt of Tanworth, honorary president of the Local Government Association.
'Above all, the new duty would remove uncertainties about local government's legitimacy in community leadership,' he said.