Björn became Minister for Iceland after Hannes Hafstein and his supporters suffered losses in the elections of 1908, where the voters rejected the draft of a new constitution.

Björn and other opponents of the Draft won a landslide victory in the 1908 elections.

Björn offended the Danish Authorities in 1909 by appointing a Councillor of Commerce to work on business negotiations for Iceland, when he appointed his supporter, Bjarni Jónsson frá Vogi, to that post.

The Danish Authorities stated that appointing such a councillor was not in harmony with the common foreign policy of Denmark and Iceland.

He died at his home in Reykjavík on 24 November 1912 after suffering a stroke few days earlier.