"We are continuing to gather information and evidence, and I think that we need to do a very thorough job there. But clearly the fact that Eritrea is providing sanctuary for terrorists is best illustrated by the report that Sheik Hassan Dahir Aweys was in Asmara [on Friday]," Frazer said.
According to Frazer, Aweys had been mentioned in a US executive order and a UN Security Council resolution for his association with al-Qaeda.
"So he's a designated terrorist attending a conference in Asmara that's supported by the [Eritrean] government."
Aweys has denied he is a terrorist or has any links with al-Qaeda.
'Terror' support denied
Meanwhile, the Ethiopian ministry of information has called for "appropriate measures" to be taken against Eritrea, for "openly pursuing its strategy of destabilising Somalia and the region".
Eritrea has described allegations that is sponsoring terrorism and destabilising the Horn of Africa region as "preposterous".
US policy toward Eritrea "has nothing to do with principles of international law or with values of justice, democracy and human rights," the ministry of information said in a statement last week.
"The United States has all along believed that its perceived strategies in the region can be better served by Ethiopia."
UN experts have found Eritrea to be the primary source of weapons and cash for fighters in Somalia, but Eritrea has denied the claim.
In August, Frazer had said that US government agencies will evaluate any evidence gathered and then a decision will be made whether to declare Eritrea a state sponsor of terrorism, a move that could impose sanctions on the country and put it in the same category as Cuba, Iran, North Korea, Sudan and Syria.
No timeline has been given for when the US will make a decision.