They are expected to centre on human rights and regional security issues, as well as the civil war in South Sudan.
Mr Obama is the first serving US leader to visit Ethiopia and will be the first to address the 54-member African Union in Addis Ababa on Tuesday.
Mr Obama flew to Ethiopia after a two-day visit to Kenya.
There he had discussed trade and security but also called for greater human rights and warned of the dangers of corruption.
The US president was greeted at Addis Ababa’s international airport on Sunday by Mr Hailemariam.
In talks on South Sudan with leaders from Ethiopia, Kenya and Uganda as well as the Sudanese foreign minister, he is expected to call for tougher sanctions and a possible arms embargo if the warring factions do not agree on a peace deal.
However, a US official travelling with Mr Obama said they were not expected to lead to a breakthrough.
“This is an opportunity to reinforce the effort that’s on the table and to strategise… on next steps in the event that it doesn’t succeed,” the official told reporters.
The 19-month war in South Sudan has left thousands of people dead and displaced more than two million.
Security issues will also be on Mr Obama’s agenda as Ethiopia, like Kenya, is battling the Somalia-based jihadist group al-Shabab.
Correspondents say he is also likely to call for greater democracy and human rights while in the country.
Ethiopia’s ruling party, the EPRDF, and its allies won every single parliamentary seat in May’s elections. Opposition parties claimed the process was rigged.
Some rights groups have criticised Mr Obama’s visit to Ethiopia, warning that the trip could lend credibility to a government accused of jailing journalists and critics.
Amnesty International’s Abdullahi Halakhe said: “We don’t want this visit to be used to sanitise an administration that has been known to violate human rights.”
Human Rights Watch and other organisations urged Mr Obama to put the “pressing human rights concerns… at the forefront of your discussions”.
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.