Vice President Mondale announced yesterday that President Carter has sent Congress the final part of his urban program, a bill to create a national development bank designed to spur private investment in declining areas.

The bank would "influence at least $16 billion in private investment - at a cost of $2 billion in federal outlays," Mondale told the 46th Annual Convention of the U.S. Conference of Mayors.

Reaction among the 250 mayors attending the convention was favorable, particularly since Mondale said the bank's aid would be "carefully targeted to communities with the greatest need."

Conference officials had lobbied hard with the administration to change the targeting formula, which at first had allowed such affluent places at San Marino and Palos Verdes Estates, Calif., to be eligible for bank aid.

Conference president Lee Alexander, mayor of Syracuse, said the proposal is "one that we can support. . . . We are pleased that the administration refined the targeting mechanism so that it more closely fits the needs of both have-not cities and cities that have real pockets of distress but generally are more affluent."

Prospects for passage of the controversial measure this year are slim. Some members of Congress have questioned whether its incentives would be enough to entice business into urban or rural slums.

Ralph Schlosstein, assistant director of Carter's domestic policy staff, conceded that it "is a most complex piece of legislation on a crowded legislative calendar. Passage clearly will take a concerted effort. It will be a very, very, very difficult thing to do."

The bank measure is the 15th piece of legislation that Carter has submitted to Congress as his urban program. Schlosstein said he is more optimistic about four other measures - supplementary fiscal aid to cities, which he called "clearly a top priority"; public works maintenance jobs; tax credit to businesses that hire longtime unemployed youths, and aid to states that help cities.

The national development bank would provide $8 billion in loan guarantees, $3.8 billion in interest-rate subsidies and $1.65 billion in grants over a three-year period.

It would work mostly with local development authorities that would submit proposals for aiding a business that wanted to expand or move into a depressed area and could create more jobs and contribute to the area's tax base.

The aid would go to some 1,800 communities with populations greater than 10,000. An added 10,000 smaller communities could qualify if they pooled their efforts and met special criteria.

Mondale's announcement, which provided the first detailed description of the proposal, said the bank would rely heavily on mayors to "identify projects and set priorities." They would designate the development authorities that would submit project applications to the bank.

Robert C. Embry, assistant secretary for community development in the Department of Housing and Urban Development, gave as an example of a business tha tmight be helped "a pic factory in Atlanta that wants to expand but can't get money from a local bank."

The national development bank could guarantee loans up to 75 percent of the long-term costs of the expansion but could provide no more than $15 million in guarantees for any one project.

It could subsidize interest rates on the long-term guaranteed debt so that the pie factory owner would pay as little as 2.5 percent. The bank could also make available grants from HUD's urban development action grant program or from the Commerce Department's Economic Development Administration.

Areas eligible for the aid would have to meet three of four criteria - a jobless rate higher than the national average, and per-capita income, population and employment growth rates lower than the national average.

Because of lobbying efforts by the Conference of Mayors, areas with per-capita income exceeding 125 percent of the national average will not be eligible. That concession knocked out more than 430 places such as San Marino and Palos Verdes Estates. CAPTION: Picture, Mondale: bank would "influence at least $16 billion in private investment." AP