The dispute over the Grand Ethiopian Renaissance Dam (GERD) has been simmering for around a decade and mediation attempts with downstream Egypt and Sudan have repeatedly failed.
"Nobody will be permitted to take a single drop of Egypt's water, otherwise the region will fall into unimaginable instability," Sisi told reporters, asked about the dam.
"Any act of hostility is detestable... but our reaction in the event that we are affected" by a reduction in Egypt's own water supply "will affect the stability of the entire region," he insisted at a news conference in the Suez city of Ismailia.
The Nile, the world's longest river, is a lifeline supplying both water and electricity to the 10 countries it traverses.
Upstream Ethiopia says the hydroelectric power produced by its dam will be vital to meet the energy needs of its 110 million people.
Egypt, which depends on the Nile for about 97 percent of its irrigation and drinking water, sees the dam as an existential threat.
Sudan, also downstream, fears its own dams will be compromised if Ethiopia proceeds with filling the GERD before a deal is reached.
Egypt's share of the Nile's waters "is a red line", Sisi said, although "we have never threatened (anyone) and I am not issuing a threat".
He made the comments as he visited the Suez Canal, a day after the crucial waterway was reopened to cargo vessels following the dislodging of a Japanese-owned megaship that had been stuck for nearly a week.
Addis Ababa announced last July it had completed its first year filling target and would proceed with the second stage, regardless of whether a tripartite agreement is in place.
Ethiopia's Prime Minister Abiy Ahmed told lawmakers last week that his country had "no intention" of harming Egypt or Sudan with the dam.
At a press conference in Addis Ababa on Tuesday, foreign ministry spokesman Dina Mufti said Ethiopia remained committed to tripartite talks involving the African Union (AU).
He had conveyed that message during a recent meeting with Donald Booth, Washington's special envoy for Sudan.
Last month, Khartoum suggested mediation by a quartet of the AU, European Union, United Nations and the United States, a proposal welcomed by Cairo but rejected by Addis Ababa.
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