Ali Abdu, Eritrea's information minister said: "We are very, very grateful to Miss Jendayi Frazer [for] exposing her ill-will towards the Eritrean people."
In July, a UN monitoring group accused Eritrea of sending large quantities of weapons to fighters in Somalia - a charge Asmara denies.
Violence has flared up in Somalia this month, with regular gun battles between Somali government forces and their main allies, Ethiopian troops, on one side and anti-government fighters on the other side.
The latter were ousted from Mogadishu in December by the combined Somali-Ethiopian forces with US intelligence backing.
Hundreds of Somalis have been killed and hundreds of thousands have fled their homes in what some analysts say is a proxy war between Ethiopia and Eritrea.
If put on the list, the country, one of the world's poorest, would join Iran, North Korea and Syria in suffering losses of US aid, US opposition to International Monetary Fund and World Bank loans and a ban on arms sales.
Frazer said Eritrea could avoid this if it stopped its activities in Somalia.
Underlining the sour relations between the former allies - Eritrea was one of only four African countries to back the US-led invasion of Iraq - Washington said this week it was shutting down an Eritrean consulate in Oakland, California.
Washington complained that Asmara was inspecting US diplomatic pouches and refusing visas for US diplomats.
Eritrea says Washington has shirked its duty to force Ethiopia, the top US counter-terrorism ally in the region, to comply with an international ruling marking its shared border with Ethiopia following a 1998-2000 border war.