"The United States, and the new administration, had hoped and frankly continues to hope that there may be a window for improved relations with Eritrea, that Eritrea may step back" from policies that fan unrest in Somalia, she said.
Should Eritrea continue with its policies in regard to Somalia, the United States could "in short order" consider steps that include "potentially, sanctions," in concert with African allies and the United Nations, Rice said.
Relations between Washington and Asmara have been poor in recent years.
Eritrea said that the US has given support to Ethiopia, Asmara's main regional rival, in a protracted dispute over the demaracation of the border.
Washington has in turn accused Eritrea of giving help to armed groups controlling swaths of southern Somalia and most of Mogadishu, the capital.
Most of the opposition fighters belong to the al-Shabab group, which is trying to bring down Somalia's transitional government and establish its own version of Islamic law.
Somalia's government and other nations have said that Eritrea has supplied arms to opposition fighters in breach of a UN embargo, claims Asmara has denied.
The African Union has called on the United Nations to impose sanctions on Eritrea for backing the rebels.