NEW YORK—Near the far end of Alex Katz’s current show at the Parrish Art Museum in Southampton, New York, is a 12-foot-wide canvas that shows yellow water lilies floating in a blue-gray pond. “It took me about 40 years to get up the nerve to paint those,” Katz admits, sitting on a couch in his fifth–floor studio in SoHo, on a weekday morning last month. “My studio in Maine is on a four-mile pond, and at the edge of it there are water lilies. People always suggested that I paint them.”

The painting is titled Homage to Monet. Entering his seventh decade of practice as an artist, Katz, 82, would certainly seemed to have earned the right to make such a tribute, though he is characteristically modest about the work. “I thought it would be more aggressive,” he says, of seeing the painting inside the hall. “But the picture’s okay. There’s nothing wrong with the painting.”

The new exhibition, which features drawings, paintings, and prints, culled largely from the past 30 years, is the latest in a series of recent shows in locations ranging from the Museo Delle Arti Catanzaro, in Italy, to the Jewish Museum in Manhattan. Late in his career, Katz is earning increasing acclaim, a rare feat in an American cultural landscape that has generally favored the young and new. The painter, though, seems largely indifferent, maybe even a little bit baffled. “I think art is as much like fashion as records or clothes,” he says. “Every three years it changes a little bit.” Among today’s fashionable artists, he cites the painters Peter Doig and Marlene Dumas as favorites.

Katz began his career as a working artist in New York at the start of the 1950s, fresh off a summer scholarship at the Skowhegan School of Painting and Sculpture in Maine. “I was in the right spot at the right time,” Katz says. It’s a remarkable statement from someone who arrived to an art world in the grips of abstraction wanting to paint cool, sober portraits. “Art usually has to do with that abrasion that gives things energy, between people and between ideas,” he explains. “With the Abstract-Expressionists, that was an abrasive thing. I had a studio next to Al Held. He had ideas, and I had ideas, and they didn’t go together, so I learned something, and he learned something.”

Indeed, Katz’s canvases would seem to be as far from Held’s packed, layered geometric abstractions as is possible. The show at the Parrish, “Alex Katz: Seeing, Drawing, Making,” includes three paintings of a single picnic table, set against a bright-green forest and a clear, blue sky. “It’s a picnic table in Maine,” he says matter-of-factly. It’s one of those visual things where you see it, and it seems ordinary and also unusual” — two perfect, apparently contradictory descriptions for Katz’s works, which, seen in a group, position him as something of an American Giorgio Morandi, the Italian still life painter who spent decades crafting spare, uncanny still lifes of bottles.

Not far from the water lilies hangs another one of those unusually ordinary works, Rain, 1989, which shows a small, blue house peeking out from a dark-gray mass of trees. Rain zips by in a few long, white diagonal lines that span nearly the entire canvas. “That is a terrific picture,” Katz admits, when prompted. “I didn’t know it was that good. Years later, people were raving about it. The colors are just from trying to match the colors I’m looking at; people don’t do that very often.” But for the small house, one would see only a near-monochrome, speckled in a few places with a few dashes of darker gray.

These blank fields of rich color, which tease toward pure abstraction, are present in many of Katz’s most recent works, like Beach, 2009, the top half of which is filled with subtly undulating shades of pale gold. Four men pose in the bottom half, on the sand, which is marked by only a few light-orange dashes. It is an enormous work, 96-by-112-inch work, and it dominates the space. “I’m trying to make them smaller, he says, only half-jokingly. “You know how you have different audiences for your paintings? These are for the painters.”