NASHVILLE, JUNE 14 -- The Reagan administration's policies toward cities came under bipartisan criticism here today as the nation's mayors gathered to adopt an urban investment policy and evaluate eight presidential candidates.

There is "an appearance of a lack of sensitivity to the people who live in the cities," said Indianapolis Mayor William H. Hudnut III, president of the National Conference of Republican Mayors. Hudnut said he was particularly angered by a Justice Department suit challenging his city's affirmative-action program -- a challenge he said cost the GOP potential support among women and minorities.

"There has been some harm done," said William J. Althaus, Republican mayor of York, Pa., citing his need to raise taxes to cover the cost of lost revenue-sharing funds and housing grants.

The Republican mayors' attacks on the administration were modest compared to the criticisms from Democrats at the 55th annual meeting of the U.S. Conference of Mayors.

"This great urban nation cannot afford the neglect our cities have experienced" under the Reagan administration, declared Joseph P. Riley Jr., Democratic mayor of Charleston, S.C., and president of the conference.

Despite the rhetoric, there was considerable evidence here of the administration's success in changing the focus on urban issues from demands for increased federal aid to more consideration of the role of the private marketplace.

Although dominated by Democrats, the conference of mayors moved toward adoption of a "national urban investment policy" that expresses its treatment of federal aid to cities in terms of its necessity for the nation to achieve international competitiveness and productivity. That approach is far different from the antipoverty arguments used to call for federal aid during the 1960s.

The policy statement "is couched in terms of competitiveness and investment because that is a reality of our times," Riley said.

The policy calls for reducing federal deficits not only through cutting military spending, but also through stemming "the growth in non-means-tested entitlements," which means such basic Democratic programs as Social Security and Medicare, although neither was named.

While urban interests may have lost power during the Reagan administration, the mayors of the nation's large cities remain targets of intense pressure from Democratic presidential candidates for endorsements.

In such cities as Birmingham, Chicago, Philadelphia and Atlanta, the black mayors are considered among the few remaining politicians in the nation who can actually deliver votes to endorsed candidates.

Six of the seven announced Democratic candidates -- all but former Arizona governor Bruce Babbitt -- are scheduled to appear here, along with two Republican candidates, television evangelist Marion G. (Pat) Robertson and former Delaware governor Pierre S. (Pete) du Pont IV.