Isaias Afwerki promised elections when he came to power in 1991 but these have still not been held.
Berhane Abrehe was Eritrea's longest serving finance minister before falling out with the president.
Men are being forced to join the army, which has been aiding neighbouring Ethiopia fight rebel forces.
"Credible reports" show they were involved in human rights abuses, the state department said.
Ethiopia's leader says Eritrea armed his troops when they first came under attack in Tigray region.
Isaias Afwerki has embraced Ethiopia's PM in a move that was unthinkable just weeks ago, but who is he?
