"The Eritrean government is not disposed to reply to such a statement by an amateur diplomat that does not reflect the U.S. administration's official stance," a statement posted on the government Web site said.
Frazer met members of Somalia's Ethiopian-backed interim government on Saturday and urged them to open the political process to all Somalis who renounced violence and extremism.
The New York Times quoted her as accusing Eritrea of destabilizing Somalia, and said it was widely known that Eritrea "would do anything" to hurt its arch foe Ethiopia.
Eritrea also said it had held talks with a former leader of Somalia's Islamists, ousted late last year in a swift offensive by Ethiopian and Somali government forces.
Asmara said in a separate statement on its www.shabait.com Web site that Sheikh Sharif Ahmed told Eritrean President Isaias Afwerki that Somalis would never submit to Ethiopian "invaders".
Ahmed said last week that his ousted Somalia Islamic Courts Council (SICC) was involved in recent battles in Mogadishu with Ethiopian forces that were described as the most violent in the capital for more than 15 years.
"We are not all prepared to allow invaders to trample upon our sacred rights and bring us under submission," he was quoted as telling Isaias.
The United Nations and United States accused Asmara of arming the SICC during the hardliner movement's six-month rule over Mogadishu and much of southern Somalia. Eritrea denied the accusations.
Washington has accused Somali Islamists of links to al Qaeda, but has said it views Ahmed -- who now lives in exile in Yemen -- as a moderate who could help national reconciliation.
In an interview last week with Al Jazeera television, Ahmed said U.S. officials had asked the Islamists to take part in a major peace meeting in the Somali capital on April 16, but as individuals not as an organization.