He is the first US leader to deliver a speech at the 54-member body, with security and action against terrorism likely to dominate the agenda.
On Monday, Mr Obama praised Ethiopia as an “outstanding partner” in taking on militant Islamists.
He said Ethiopia had weakened al-Qaeda-linked al-Shabab group in Somalia.
The US president was speaking after talks with Ethiopia’s PM Hailemariam Desalegn, during the first ever visit by a US president to the East African state.
He also called on Mr Hailemariam to improve Ethiopia’s record on human rights and good governance.
“I don’t bite my tongue too much when it comes to these issues,” he said at a joint press conference in the capital, Addis Ababa.
Some rights groups have criticised Mr Obama’s visit, warning that it could lend credibility to a government accused of jailing journalists and critics.
A legal case currently being fought through the US courts alleges that agents of the Ethiopian government eavesdropped on the internet activities of a man in the US state of Maryland.
The man, born in Ethiopia and now a US citizen, works for a political opposition group outlawed in his home country.
Addressing the media, Mr Obama described the Ethiopian government, which won all parliamentary seats in May’s election, as “democratically elected”.
Opposition group have said the poll was rigged.
Mr Obama flew to Ethiopia after a two-day visit to Kenya where he had discussed trade and security but also called for greater human rights and warned of the dangers of corruption.