President Carter told the North Atlantic Treaty Organization today that the United States is sending more troops to Europe and that the budget proposals he will make to Congress this month will "provide for real increases in U.S. defense spending."

Winding up his whirlwind tour of seven nations, the President visited two symbols of European unity and the continent's ties to the United States - the headquarters of NATO and of the European Economic Community (Common Market).

Carter did not specify how much of an increase in defense spending he will recommend to Congress. But contrary to his campaign promises to cut defense spending, the emphasis in his remarks to NATO was on an apparently significant increase in defense spending.

"The defense budget that I will be submitting to the Congress later this month will provide for real increase in U.S. defense spending, more than compensating for the effects of inflation," he said.

The President said that over the next year and a half the United States will send more than 8,000 additional military personnel to Europe and will "substantially improve our reinforcement capability."

U.S. officials said later that the troop increase has been planned for some time and will bring the American troops in Europe to their fully authorized force levels.

It was the first time that specific figures for the net increase to be reached by the end of fiscal 1979 were disclosed. Besides bringing maneuver battalions up to the scheduled strength, U.S. officials said later, the Pentagon's program calls for adding artillery units and Cobra helicopter gunships to the 190,000-strong U.S. Army force in Europe.

Carter's defense budget for fiscal 1979 calls for $126 billion, or nearly $10 billion more than the defense spending Congress approved for fiscal 1978. The Pentagon had asked for $130 billion, but the President had pared down that figure by $4 billion.He has approved increases for NATO reimpact forces but cut other programs.

During his Presidential election campaign, Carter said he though $5 billion to $7 billion a year could be cut from the defense budget, a pledge that the administration is finding difficult to fulfill.

Carter made these announcements in a speech in which he also said he hoped there would be progress this year toward a new strategic arms limitation agreement with the Soviet Union and in the negotiations with the Warsaw Pact nations of Eastern Europe over troop level reductions.

American officials said Carter sought in his remarks to reaffirm the United States' willingness to continue spending billions of dollars on NATO should the troop reduction talks remain stalled.

"We will work with you to maintain deterrence across the entire spectrum of strategic theater, nuclear and conventional forces, so that the Warsaw Pact states will know that all of us are united in commitment to defense of all the territories of NATO members," the President said.

"There will be no flagging of American will or ability to meet all of our NATO commitments, which have the firm support of the American people," he added.

Carter also struck one of the major themes of his foreign trip.

"Lastly, as allies, we must continue to promote our strength in other areas - economic, political, social moral," he said. "It is precisely when the challenge to democracy is greatest that our leaders must most firmly resist nondemocratic solutions."

The President remarks to the 14 permanent NATO representatives were made behind closed doors, and reporters were given a text of what he planned to say. In the prepared text, there was no mention of the neutron bomb and its possible deployment in Western Europe, a major controversy here.

After a state lunch will Belgium's King Baudouin, Carter met with Roy Jenkins, president of the EEC Commission, before going on to NATO.

In remarks to the Common Market ministers, he stressed the need for new trade agreements and the dangers posed to the international economy by protectionism.

Carter left Brussels early tonight and landed at Andrews Air Force Base at 8:49 p.m., EST.

The President flew here this morning from Paris, where he met with French Socialist Party leader Francois Mitterrand at the residence of U.S. ambassador Arthur Hartman.

While Carter appeared to go out of his way to avoid any suggestion of meddling in internal French politics - he declined to visit the Paris city hall and thus offended Mayor Jacques Chirac, a Gaullist - his meeting with Mitterrand surprised and puzzled political observers here.

Last year, when Mitterrand wanted to visit Washington for talks with Carter, the White House in effect discouraged the French politician by saying that it could not guarantee his appointment with the President. Subseqently, Mitterand canceled his already announced trip.

Mitterrand asked for today's meeting, during which, according to a White House official, Carter expressed his "concern" over the possibility that European Socialists would align themselves with the Communists.

With reporters present for the beginning of the meeting, the President had kind words for Mitterrand.

"You have played a good and beneficial role in France," he said. "It is a great honor to meet you. We have many things in common."

Mitterrand's Socialists party represents the greatest single threat to the coalition led by President Valery Giscard d'Estaing in the French legislative elections scheduled for March. Carter's visit to Paris was interpreted in some quarters as an attempt to give Giscard a boost shortly before the elections.

Following the meeting, Mitterrand told reporters:

"I think my role will have been beneficial if it takes the hopes of the French people to power, if it assures the success of the profound aspiration of the French left. But that success is completely compatible with an international policy and concord with the American people who are our traditional friends. That is why contact and improved understanding between the leaders is important."

The President's visit to Belgium was prefunctory at most, lasting less than seven hours. Its chief purpose was symbolic - an attempt to demonstrate American support for European untiy and the American commitment to European defense.

The visit came near the end of Carter's first extensive foreign tour, a grueling journey of 18,000 miles that took him to seven countries in nine days. Beginning Dec. 29, the president visited Poland, Iran, India, Saudi Arabia, Egypt, France and Belgium.

The stop in Egypt for a hastily scheduled meeting with Egyptian President Anwar Sadat, while the briefest, was also probaby the most important. What effect that meeting will have on the Middle East peace negotiations along with the impact of the trip as a whole, remained largely a mystery to those traveling with the President today as the American party prepared to head home.

As the journey neared its end, White House officials sought to give it the most positive interpretation.

"I think the President has found the trip to be extremely enjoyable," White House press secretary Jody Powell said last night in Paris.

"I think those of you that have watched him on public occasions could easily deduce that it was not only personally enjoyable for himself and for Mrs. Carter but also quite constructive with regard to the numerous issues which have been pursued in the various meetings on the trip," he added.

At Brussels' airport this morning Carter talked about his trip as a whole.

"This has been a diverse journey for us but I have talked about simple, constant themes," he said.

"One is the demand for political liberties, for basic human rights. On this question, Belgium and the United States have never differed. For these values we have fought together in war, and we have always worked together in peace.

"The other universal theme is a need to resolve conflict without violence, to make peace instead of war," he continued. "Throughout this century, Belgium has paid a heavy price for other nations' failure to keep the peace. Now Brussels is the home of institutions such as the European Community, and NATO represents our shared hope for a secure and peaceful and a prosperous future.