Before the talks on Thursday, Mrs Clinton honoured the victims of the August 1998 attacks on the US embassies in Kenya and Tanzania, in a wreath-laying ceremony in Nairobi.US Secretary of State Hillary Clinton has warned that the US will "take action" against Eritrea if it does not stop supporting militants in Somalia.
She said after talks with Somali President Sheikh Sharif Sheikh Ahmed in Kenya's capital, Nairobi, that Eritrea's actions were "unacceptable".
She also said the US would expand support for Somalia's unity government.
Eritrea denies supporting Somalia's al-Shabab militants, who are trying to overthrow Somalia's government.
Al-Shabab is growing in strength and 250,000 Somalis have fled their homes in fighting between militants and government forces over the past three months.
More than 220 people were killed and 5,000 injured in the first major attack by al-Qaeda on US targets.
AP news agency quoted her as saying that the embassy site was a reminder of "the continuing threat of terrorism, which respects no boundaries, no race, ethnicity or religion, but is aimed at disrupting and denying the opportunity of people to make their own decisions and to lead their own lives".
BBC NEWS | Africa | Clinton threatens Eritrea action