The Wednesday attack sparked a skirmish that left at least one attacker dead, according to the US military.
Around a dozen guerrillas attacked the outpost at Nangalam, about 170km east of the capital Kabul in Kunar province.
Military spokesman Lt Colonel Bryan Hilferty said the attackers fired about 20 rockets before opening fire on the base, which houses approximately 100 US marines and special forces.
Trail of blood
There were no reports of any American casualties and US forces responded with an A-10 ground attack aircraft.
"We discovered blood moving into the hills, so it appeared that some of the enemy were wounded."
The province's governor, Faisal Akbar, said an Afghan civilian died in the crossfire.
Kunar is the northernmost of a string of troubled Afghan provinces along the border with Pakistan where the 13,000-strong US-led coalition is focusing its campaign to destroy the Taliban and al-Qaida.
In a separate incident in Kandahar, attackers fired three rockets at the US's main military base in southern Afghanistan, hitting the grounds but causing no injuries.
Qalb al-Din Hekmatyar supporters
are fighting alongside ex-Taliban
Khalid Pashtun, spokesman for the Kandahar provincial government, blamed the Taliban for the attack, which occurred shortly after midnight on Tuesday.
Attackers fired their rockets from a position at Khushab village, west of the Kandahar airport. The airport is a base for US offensive aircraft.
A search of the site where the attack was launched found a cache of 22 other rockets, but no arrests have been made.
American military officials at the base were not prepared to comment on the incident.
But remnants of the Taliban government ousted by an assault in late 2001 are believed to have teamed up with al-Qaida and fighters loyal to Qalb al-Din Hekmatyar to fight the US-backed government of Hamid Karzai.
At least 140 people have died in violence in Afghanistan so far this year, including aid workers and government employees as well as Afghan and international troops and rebel fighters.