How did the US government respond to the immigration wave in the late 1800s?

Laws were passed to limit diversity among the immigrant population.

on edg2020

Immigration had already been opposed by the Nativist Know Nothing movement of the 1850s. This movement opposed the immigration of Irish and German Catholics on grounds of their religion. As of the 1870s the shift from a sail transportation maritime system to a steam powered one made it possible for transportation companies to bring in large numbers of immigrants more often and faster than ever before.

Due to the railroad construction and the desire for docile; low-wage workers, employers stated recruiting people from Asia, especially China. In 1875, the Asian Exclusion Act was passed in order to forbid the hiring of Asian unskilled workers and women who were considered as potential prostitutes. It was followed by the Chinese Exclusion Act which severely restricted Chinese immigration to the US for ten years. The act was renewed and expanded in 1892 and 1902.