How did the federal government try to ease the tensions between American settlers and Native Americans?

The Federal Government issued the Indian Appropriations Act of 1851, thus keeping the Indians away from the lands that American settlers wanted to occupy.

Explanation:

After the discovery of a vast, seemingly unoccupied territory, the American settlers wanted to establish in the regions that belonged to the Indian tribes. The Indian removal act of 1830 authorized the forced removal of the Indians from their homelands in the southeast, to what was designated as the "Indian territory", west of the Mississippi River. The Cherokee people were submitted to a mass exile that was later known as the infamous Trail of Tears. This forced attempts to remove the Indians from their lands, led to years of wars and bloodshed between native Americans and settlers.

The peaceful solution took place when the Indian Appropriations Act of 1851 was issued, and the Indians were allowed to move willingly to the regions now known as the states of Oklahoma, Nebraska, and Kansas. There were even given monetary compensation for their lands. This, however, was not enough, as some Indian tribes still resisted the Act. The Indian wars finally ended with the Battle of the Little Bighorn, which was the last major conflict between natives and settlers.

The government restricted the reservation lands by setting boundaries for each tribe