It is a curious film in that regard, as it is hard to firmly label Saving Private Ryan as a pro-war film in the vein of Bataan or The Green Berets, or an anti-war film like Paths of Glory. It is not hard to see inspiration from both sides. The entire structure of the film's narrative, which centres around the camaraderie between a diverse group of men with an emphasis on heroics, is easily lifted from the World War II combat films produced in Hollywood during the 1940's. On the other hand, the harsh battle sequences could easily have drawn from the likes of Paths of Glory. There is a patriotic tone to the overall movie, which is even bracketed by a shot of an American flag, but at the same time there seems to be something else.
There is definitely a sense that the film intends the viewer to respect the soldiers, but it is worth noting that Saving Private Ryan makes no effort to cover up the horrors of war. The famous Omaha Beach sequence has no trouble emphasizing the thousands of American soldiers who don't survive. There are even realistic depictions of gunshot wounds, and many of them are obviously scared even before the Normandy invasion begins, and when they are being shot at, many of them are more concerned about their immediate survival than ultimately winning the war.
While the focus is purely on the American military (nothing is shown of the Canadians or Brits who also participated in the D-Day invasion), it is hardly glorified. In fact, Saving Private Ryan seems to deliberately emphasize that World War II was not black and white. Most of the few enemy soldiers depicted are shown to be frightened human beings not much different from the Americans. The Americans are also shown to not be above committing war crimes, as is evident when after taking Normandy they proceed to execute soldiers who are obviously trying to surrender and even joke about it.
Even the one German who directly confronts any of the Americans, credited as "Steamboat Willie" (Joerg Stadler) is obviously just a man following orders. When he survives their raid on his machine gun nest, he is simply scared for his life and begs to spared. He is also clearly nervous when he is forced to dig graves, and knows the implications of being forced to do so. This is just an ordinary man trying to survive, not much different from any of the American soldiers. It is true that he later shows up at the end of the film and shoots Captain Miller, but this is likely nothing more than an unfortunate coincidence.
Of course, Saving Private Ryan is not completely anti-war. Spielberg obviously made this film with the intent of respecting fallen soldiers, and there is a sense of victory (if at a cost) which emerges at the end. The war is hardly glorified, but it does appear to suggest at least America's participation was not unjustified, and that good did come out of it. This makes it a curious experience to watch, as Spielberg seems to be intent on showing both sides of the war, the good and bad.