In addition to the grants otherwise authorized by this chapter, the Secretary is authorized to make a grant for the purpose of increasing the Federal contribution to a public works project for which Federal financial assistance is authorized under provisions of law other than this chapter. Any grant made for a public works project under this section shall be in such amount as may be necessary to make the Federal share of the cost of such project 100 per centum. No grant shall be made for a project under this section unless the Federal financial assistance for such project authorized under provisions of law other than this chapter is immediately available for such project and construction of such project has not yet been initiated because of lack of funding for the non-Federal share.