It was the second time that Frazer had publicly spoken of the evidence her country says it is compiling of alleged Eritrean support of al-Qaeda-linked Muslim fighters in Somalia.
On August 17, Frazer said US government agencies will evaluate any evidence gathered and then a decision will be made whether to declare Eritrea a "state sponsor of terrorism".
Such a move that would impose severe sanctions on the impoverished nation and put it in the same pariah category as Cuba, Iran, North Korea, Sudan and Syria.
No deadline has been given for when the US may make such a designation.
The Eritrean government has previously said US policy towards Eritrea "has nothing to do with principles of international law or with values of justice, democracy and human rights".
It said the US "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 armed Muslim groups in Somalia, something Eritrea has denied.
The US suggested on Saturday that evidence of Eritrean support for extremists includes a conference of Somali dissidents that Eritrea is currently hosting that includes individuals who have been linked to al-Qaeda.
Frazer said: "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 Sheikh Hassan Dahir Aweys was in Asmara yesterday."
Aweys has been singled out in a US executive order and a UN Security Council resolution for his association with al-Qaeda, Frazer said.
Aweys has denied he is a terrorist or has any links with al-Qaeda.
Aweys's group, known as the Union of Islamic Courts, ruled Somalia's capital and much of southern Somalia for six months last year.
Ethiopian forces, backing Somali troops, drove it out in December.
Remnants of the group have launched a violent campaign against the UN-backed Somali transitional government.
In the latest incident, five Somalis were killed on Saturday in Mogadishu's Bakara market area as police were conferring with locals on ways to make the locality secure, witnesses and security sources said.
A witness told the AFP news agency that asssailants shot down two people in the sprawling area's Abdala Shideye district.