War has broken out among the nation's cities.

It pits communities in the Sun Belt against those in the Frost Belt in an effort to grab what they perceive to be dwindling federal aid.

Only a few years ago the battle lines in the fight for then-expanding federal aid tended to be drawn between cities and their more affluent suburbs or, to a lesser degree, between big cities and little cities.

Now regional differences are paramount, and the Southwest is accusing President Carter of tilting his urban programs to favor the older cities of the Northeast.

"The debate between the regions has always existed," says Alan Beals, executive director of the National League of Cities. But it was subdued because the federal aid pot kept expanding. Now the pot is being limited, so the debate is more intense."

The Sun Belt-Frost, Belt fight almost caused a major split in another urban organization, the U.S. Conference of Mayors, this summer.

And the National Leaque of Cities, which represents about 800 cities, deems the controversy so important that it opened its 55th annual convention here today with a discussion of the monetary stakes at issue.

Mayor Hugh Parmer of Fort Worth, a leading Sun Belt spokesman, said his region fears it will be hurt by Carter's programs to promote business growth in "distressed" areas.

"Distressed" is defined differently in different programs. If often refers to older cities that have lost manufacturing jobs, and while the Sun Belt has such cities, the North and East have many more.

Parmer said economic development aid "is the basic problem" between the regions, "and I don't think it's resolved."

He also said Carter's loss in Congress this year of a program to continue federal aid to cities with high jobless rates "might have been prevented if the program had been more palatable to the South and the West."

Nothing reports that Carter wants to cut the 1980 federal budget by $30 billion, Parmer said, "If the Southwest and Northeast do not reach an understanding, it will be a loss to all the cities of the nation. . .

"The political reality is that representatives of the South and West are not willing to consider programs which continue to aid only Northeastern states until the Southwestern problems are also acknowledged and included in the criteria for federal funding."

Parmer said "some northern groups" are seeking to change the formula for distributing federal revenue sharing money to localities so that more would go to be Northeast.

"This would result in a reduction of the allocation to southeastern cities," the major said. "I would like to emphasize that revenue sharing is the life blood of our cities and we will not passively accept cuts in such a vital program."

The federal government now spends $6.6 billion on revenue sharing and sends money to communities on the basis of their population, per capital income and local tax effort. In relation to the rest of the country, the Sun Belt has done well in revenue sharing allocations.

Christopher Lindley, a member of the Rochester, N.Y., city council and spokesman for the Frost Belt, agreed that the formula should should not be changed "If we split over the formula, we'll end up with no formula," he said.

Lindley also agreed with Parmer's comment that many Sun Belt cities have "pockets of poverty." But he argued that northern and eastern localities spend an average of $2,400 a year on each poor person while those in the South and West spend only $800 a year. A federal government reimburses the Northeast for about half those costs while it reimburses the South and West for more than 60 percent of them, he said.

Lindley accused the Sun Belt of asking for federal funds to meet the "stress of raising local taxes to finance essentially local services in communities which are fully capable of paying for those services in the absence of federal assistance."

The councilman also proposed that federal aid formulas take into account the differences in the cost of living throughout the country. Such a change presumably would benefit many northeastern cities.