Ethiopia's government admitted on Tuesday to firing on a United Nations team who were visiting refugees in the conflict-hit Tigray region.
But a government spokesman said they were to blame for Sunday's incident close to the town of Shire, claiming they ignored instructions and drove through government checkpoints.
UN and aid agencies are continuing to seek access to the region a week after fighting there was declared over.
"They broke two checkpoints to drive hastily to areas where they were not supposed to go, that they were told not to go," Ethiopian government spokesman Redwan Hussein told a press conference.
"They were left alone when (and) they broke two checkpoints, and when they were about to break the third one, they were shot at and detained. Now, of course they are free."
"This country isn't no man's land. It has a government," he added.
Almost one million displaced
Ethiopia's army has battled the Tigray People’s Liberation Front (TPLF) in the northern region since November 4.
Thousands have been killed and the UN estimates that more than 950,000 people have been displaced by the conflict,
UN spokesman Stephane Dujarric said there were four people in the UN team assessing roads in the area for aid deliveries.
Last week the UN said it had signed an agreement with the Ethiopian government guaranteeing "unconditional access for humanitarian assistance".
But Dujarric said the pact was not being met.
"Are we getting unfettered, clear humanitarian access at this point? No. And that's why we're still in discussions with the government to try to get to where we want to be," he said.
"We do have a number of humanitarian workers that stayed behind. I think most of them, if not all of them, nationals, they're trying the best that they can. But clearly, we're not able at this very moment to get the aid that we want to get in."