The House Budget Committee, which Wednesday night rejected President Carter's long-awaited national urban and rural economic development program, yesterday reversed itself and gave final approval to most of the President's request.

The committee, at the initiative of Rep. Stephen J. Solarz (D-N.Y.), reinstated $500 million of $788 million in authority that would have financed $2 billion in a new program of grants, loan guarantees and interest subsidies to stimulate economic development in distressed urban and rural communitites.

The committee's rejection Wednesday came shortly after the President announced his sscaled-down program-a revision of his controversial proposal for a National Development Bank. That project was strongly resisted on Capitol Hill last year and later dropped by Carter.

The committee, however, was unaware of Carter's program before Rep. James R. Jones (D-Okla.) suggested that $1.5 billion in authority already set aside for the program be rejected. Jones said the Commerce Department's Economic Development Administration, which was to run most of the program, did not need that much money and that Carter had not told them what he specifically wanted to do with it.

The committee left intact a $275 million authority for a grants program to be run by the Department of Housing and Urban Development, a small part of the total effort.

"That budget committee had not had that legislation until today (Thursday)," an EDA spokesperson said. EDA officials earlier had "breifed people on the Hill" about the legislation but they had not expected the committee to act on it until Friday, the spokesperson said. "Congress and the White House work very independently," she added.

"We are pleased, very pleased," said Beverly Milkman, an EDA official.

The National Governor's Association, however, said the President's proposal would increase the federal bureaucracy unnecessarily.

"It would continue to exclude the states from playing a strong role in federal economic development programs," said Delaware Gov. Pierre DuPont, chairman of the association's economic development committee. "EDA will have substantially greater loan and grant authority and will attempt to administer economic development programs involving tens of thousands of local jurisdictions directly from Washington."

The plan, which EDA officials said was intended to give local governments and businesses more say in the programs in their area, highlights a program to provide more that $3 billion in direct and tax expenditures and almost $3 billion in loan guarantees to stimulate private sector jobs and investment in economically distressed communities.