Ethiopia last week accused Trump of inciting a "war" over the Grand Ethiopian Renaissance Dam (GERD) after the U.S. president on Friday spoke out against the project and said Egypt might destroy it.
This comes two days after Ethiopia summoned the US ambassador following what it described as "incitement to war" between Ethiopia and Egypt by US President Donald Trump.
On Monday, Ethiopian MPs said that "no force on the face of the earth" will stop the completion of the dam and that they were ready to defend it from both internal and external attacks.
Further, both organisations highlight that they have also worked with many United States experts who have helped to strengthen this message.
Ethiopia built the GERD to supply hydroelectric power to its population of more than 100 million.
The statement added, "Sudan will participate in Tuesday's meeting to discuss negotiation methods different to those followed in the last round, by granting a bigger and more effective role for experts and observers".
The president was on the phone to Sudan's Prime Minister Abdalla Hamdok and Israel's PM Benjamin Netanyahu in front of reporters at the White House on Friday.
Sudan is cautious heading into Tuesday's negotiations. Ethiopia walked away from those talks.
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Without mentioning Trump or the US, the office of Ethiopian Prime Minister Abiy Ahmed issued a separate critical statement amid an outcry in Ethiopia over Trump's latest threat regarding the dam.
Threats of any kind over the issue were "misguided, unproductive and clear violations of global law".
The statement by Abiy's office said the talks with Egypt and Sudan have shown significant progress since the African Union has stepped in to oversee them.
He added: "Ethiopia will not cave-in to aggressions of any kind, nor do we give recognition to a right that is entirely based on colonial treaties".
There was no comment from the Egyptian government on Trump's remarks, but pro-government media covered them extensively.
It is being seen as an existential threat for the very survival of Ethiopia as a developing country.
Trump's new remarks have prompted some Ethiopians to urge Ethiopian Americans to vote against the president him in next month's election. The AU, he said, remains seized of the GERD matter. Ethiopia rejects binding arbitration at the final stage. "It will affect thousands of people along the way if this huge amount of water gushes out of the dam".
Ethiopia, which announced the start of construction in 2011, says it needs the dam for its economic development.