The Israeli Cabinet today approved in principle a controversial plan to construct a 61-mile canal from the Mediterranean Sea to the Dead Sea, providing hydroelectric power and raising the level of the Dead Sea.

The $700-million canal, which would be financed by foreign investment, is tentaviely charted to cut through the occupied Gaza Strip. But Israel planners have devised an alternate route to be used if "political considerations" arising from a negotiated settlement of the Gaza Strip's status bar the original plan. The alternate route would add $60 million to the project.

The Gaza Strip was administered by Egypt before Israel captured it in the 1967 Six-Day War, and its status is an issue of the now-stalled Egyptian-Israeli negotiations focused on Palestinian autonomy.

Gaza Mayor Rashid Shawa protested the plan today, saying, "The Israeli government has no right to make a decision on a plan which infringes on the territory of Gaza."

The canal, which would take three years to plan and another four to six years to construct, is also expected to raise legal problems with Jordan because the massive inflow of water would raise the level of the Dead Sea an estimated 56 feet and would force Jordan to move its mineral mining works, now on the eastern shore of the sea.

However, Yuval Neeman, chairman of a public steering committee that is planning the canal, said Jordan would benefit from the project and Israel would only be required to initiate "techinical contact" between foreign companies building the waterway and the government of Jordan.

He noted that evaporation had lowered the level of the Dead Sea to the point that it is possible to walk across it in some spots, and that raising the level would boost the capabilities of potash works on both sides.

Critics of the canal have also noted that ecologists have yet to sort out the possible effects of mixing Mediterranean Sea water with the densely salinated and heavily mineralized water of the Dead Sea.

But the Cabinet instructed the steering committee to step up its feasibility study of the waterway, dubbed the "Med-Dead Canal." It also ordered Finance Minister Igael Hurwitz to explore its financing.

The Cabinet ministers recommended that the committee concentrate on the route that would start at the Gaza strip village of Katif, just north of Khan Yunis, and run in a southeast direction across the Negev Desert to a point southeast of Beersheba.

Then it would veer slightly northeast to Ein Bokek, where a hydroelectric generating plant would be built.

Because the Dead Sea is about 1,300 feet below sea level, the drop would generate 600 megawatts of electricity, or 23 percent of the 2,600 megawatts consumed annually. By 1990, Israel's yearly consumption will be about 4,000 megawatts, meaning that the canal could supply 15 percent of the need, according to Neeman. Officials estimate Isreal could save up to $100 million a year in fuel costs.

Newman said that until now the plan was not considered economical, but that the soaring world fuel price had made it feasible. He said foreign investors could be lured if they were allowed to run the power plant, which could bring in an estimated profit of more than $1 billion during a 50-year period.

The canal's route through the largely uninhabited desert also raises the possibility that its water could be used to cool a nuclear power plant along the way, officials said.

In a news conference, Energy Minister Yithak Modal said a Canadian investor had already expressed interest but Modai would not identify him.

The idea of a sea-to-sea canal was first proposed by Theodore Herzl, the founder of Zionism, in an idyllic novel entitled "Altneuland" (Old New Land). He described how a new Jewish state would transform the then barren Palestine. The plan was suggested to Herzl by a Swiss engineer, Max Bourcart, who proposed a two-canal system to provide electricity and fresh water.

Bourcart envisioned a fresh-ater canal from the Sea of Galilee south through the Samarian hills, and seawater canal from Haifa through the Jezreel Valley and to the Jordan River, which in turn flows into the Dead Sea.

One of the three plans that has been under study by the Israeli steering committee followed Herzl's Jezreel Valley scheme, dumping Mediterranean Sea water into the Jordan River at a point below where Israel and Jordan tap the river for fresh water.

But the route would cut across the West Bank and would complicate the Middle East peace negotiations.

The plan favored by the Cabinet envisions a 13-mile open canal from Katif to a point near the Negev town of Besor, followed by a 48-mile tunnel about 18 feet n diameter and sunk as much as 1,300 deep in the ground.