"We have turned the corner" in strengthening the North Atlantic Treaty Organization. Gen. Alexander M. Haig Jr. said yesterday in giving a generally upbeat report to the Senate on the state of the alliance.

"I think we have great cause for cautious optimism," said Haig, commander of U.S. forces in Europe, despite "rough spots and some worrisome nations" within the alliance.

He based his optimism on the additional investments NATO members are making in alliance military forces, with the 3 percent increase in President Carter's fiscal 1979 budget for NATO-related activities an example of the unward swing.

On the negative side, Haig told the Senate Armed Services Committee, the "area of greatest concern remains the eastern Mediterranean," with congressional limits on U.S. arms to Turkey "very worrisome."

Haig said "I'm not sure" Turkey will not turn to another country for its arms if the United States refuses to supply them.

Haig's "turn the corner" expression, shunned by most generals since it went sour during the Vietnam war was contained in one of several written statements to the committee portraying a steadily improving NATO force.

Robert W. Komer, formerly head of pacification in Vietnam and now adviser to Defense Secretary Harold Brown on NATO affairs, said in his statement that "when one looks at all aspects, it is hard to avoid the conclusion that our allies are making a NATO effort roughly comparable to ours."

Gen. Bernard W. Rogers, Army chief of staff, said the Army's upgrading effort for NATO has these four "basic thrusts": improve warning time; strengthen forces along the Nato front; improve the reinforcement structure; and dovetail U.S. defenses with allied ones.

Military leaders made these other points during the Senate hearing on NATO:

Marines -- The Corps, at the request of Secretary Brown, is studying the possibility of basing more Marines within easy striking distance of NATO.

Neutron bomb Haig said "the majority" of European military commanders regard the neutron bomb as a desirable "modernization," but its deployment is a political question.

Cruise missile -- Several NATO countries will at least "flirt" with the idea of building their own ground-based cruise missiles, but "I have yet to see the data that would convince me it is the answer to a maiden's prayer," Haig said.

German tank gun -- Rogers said the Army hopes to buy 7,050 XM1 tanks for NATO, with the first 2,000 of them armed with the U.S. 105 mm gun. The decision on how many of the remaining tanks will get the German 120 mm gun will be made in the light of information not yet in hand, although Pentagon officials envision a sizable purchase.

Non-nuclear Lance battlefield missile -- "We need it," said Rogers.

While the Senate was getting its report on NATO, Brown was justifying the Pentagon's $126 billion request for fiscal 1979 to a House Budget subcommittee.

Subcommittee Chairman Robert L. Leggett (D-Calif.) congratulated Brown for a low-key description of the Soviet threat. "I don't think you need to paint the Soviet Union 14 feet tall to get the Congress" to beef up U.S. defenses, Leggett said.

Brown, while stating that the Soviet Union is outspending the United States by 20 to 40 percent for defense, said the Russians suffer "major internal handicaps."

Said Brown: "These handicaps will probably increase with the decline already occurring in birth rates and about to begin in domestic energy supplies and rates of economic growth."

Gen. David C. Jones, Air Force chief of staff who appeared with Brown before the House subcommittee, said the Air Force still has the option to produce the B1 or other bombers if the strategic situation changes dramatically.