Obama is on the first-ever trip by a US president to Africa's second most populous nation, a close strategic partner for Washington credited for beating back the Al-Qaeda-affiliated Islamists but a country also much criticised for its rights record.
"Part of the reasons we've seen this shrinkage of Shebab in East Africa is that we've had our regional teams," Obama said, referring to African Union and Somali government troops.
"We don't need to send our own Marines in to do the fighting: the Ethiopians are tough fighters," Obama said, adding: "We've got more work to do we have to now keep the pressure on."
While the United States does not have boots on the ground, it carries out frequent drone strikes against Shebab leaders.
Speaking after talks with Ethiopian Prime Minister Hailemariam Desalegn, whose ruling party won 100 percent of seats in parliament two months ago, Obama gave the blunt message that the country -- while credited with strong economic growth -- needed to perform better on basic rights.
"There is still more work to do, and I think the prime minister is the first to admit there is still more to do," Obama said.
"There are certain principles we think have to be upheld," Obama added. "Nobody questions our need to engage with large countries where we may have differences on these issues. We don't advance or improve these issues by staying away."
Hailemariam, however, pushed back against criticism his government has quashed opposition voices and suppressed press freedom.
"Our commitment to democracy is real and not skin deep," he insisted, adding that Ethiopia is a "fledgling democracy, we are coming out of centuries of undemocratic practices".
"For us it's very important to be criticised, because we also get feedback to correct our mistakes. Media is one of the institutions that have to be nurtured for democracy," Hailemariam said.
Obama flew into a rainy Addis Ababa late yesterday after a landmark trip to Kenya, his father's birthplace, where he spoke frankly on human rights and corruption.
Talks were held today in Ethiopia's presidential palace, a sprawling compound in the heart of Addis Ababa, which still houses the country's unique black-maned Abyssinian lions in the grounds, once the symbol of the "Lion of Judah", former Emperor Haile Selassie.
