Ethiopia began rerouting water from the Blue Nile last week for the $4.7 billion project, the Great Ethiopian Renaissance Dam.
The project is expected to be completed by 2017.
Although the construction started two years ago, tensions between Egypt and Ethiopia over the dam are just now becoming public, Voice of America reported.
Last week, Egypt's government said it did not approve of the building of the dam.
A spokesman for the Ethiopian Ministry of Foreign Affairs, Dina Mufti, said the country will not consider halting the construction.
Egyptian politicians were overheard on a live broadcast discussing ways to sabotage the project, Voice of America said.
Ethiopia demanded an explanation from the Egyptian ambassador this week.
"We are caught by surprise because some government officials, party leaders and civil society leaders, they were talking about Ethiopia violently and we were surprised. We are waiting for this tone to be watered down very soon," Mufti said.