Overcoming West European resistence, the Reagan administrative today won a renewed commitment from members of the North Atlantic Treaty Organization to increase their national defense spending by 3 percent a year in real terms through 1988, according to senior alliance officials.

Senior U.S. defense officials claimed victory after the first day of a two-day meeting of NATO defense ministers, although it remained questionable whether the commitments made today could be honored in the near term, given the current financial difficulties of some West European countries and the past dissatisfaction voiced by their governments with such fixed spending targets. The 3 percent figure is to be in addition to whatever the inflationary increase is.

U.S. Defense Secretary Caspar W. Weinberger, in a closed-door meeting, backed a call for additional NATO spending with a dramatic presentation outlining the growth of Soviet conventional military might in the past decade, officials said.

Allied officials said the U.S. team also held tough negotiations on spending pledges for NATO's infrastructure program, which funds basic military facilities in Europe.

The ministers eventually compromised on a one-year funding figure. West German Defense Minister Hans Apel, who was said by another European minister to have pushed hardest for a lower spending figure, told reporters afterward that the debate involved "hard arguing."

Apel is already in political trouble in Bonn as a result of budget short-falls. He and Weinberger were reported by aides to have aired their differences at a bilateral meeting this morning, although both American and West German offocials later played down the degree of disagreement.

The arguments over spending reflected a basic difference in priorities at the moment between the Reagan administration, whose key aim is to build up defense, and the majority of West European governments, which would prefer to get more for existing defense dollars.

U.S. officials played up the Soviet threat in a classified briefing delivered by a Pentagon intelligence expert. The NATO ministers received what a senior U.S. official called "a grim story" of increased Soviet conventional military capability.

American officials said the briefing was more extensive than that available normally to European governments. Weinberger had provided a similar briefing to NATO defense ministers on Moscow's strategic capabilities at a meeting of the Nuclear Planning Group last month.

Today's presentation stressed advances in Soviet ground, air and naval forces, made possibly by what U.S. officials described as the Soviet Union's growing military industrial base. This was said to include 134 plants now operating with more than 40 million square yards of floor space -- a 34 percent increase since 1970, according to a U.S. official.

While Warsaw Pact conventional forces have long outnumbered NATO's, the West once could count on its higher-quality weapons to offset Soviet armaments.

But Weinberger told the NATO meeting today that this was no longer true, U.S. officials said.

Weinberger urged reaffirmation of the 3 percent annual growth figure agreed to by NATO allies in 1977 to fund a series of long-term NATO defense goals approved that year, U.S. officials said.