Operation Lüttich (7–13 August 1944) was the codename of the Nazi German counter-attack during the Operation Overlord, which occurred near U.S. positions near Mortain, in northwestern France. Lüttich is the German name for the city of Liège, Belgium. In British and American histories of the Second World War, the German Operation Lüttich is known as the Mortain counter-attack, which Hitler ordered to regain territory gained by the First United States Army during Operation Cobra by reaching the coast of the Avranches region, which is at the base of the Cotentin peninsula, in order to isolate the units of the Third United States Army that had advanced into Brittany.

The Germans' main force was the XLVII Panzer Corps, with two Heer and one-and-a-half Waffen-SS Panzer Divisions. Despite initial success against the defending U.S. VII Corps, the Germans were soon halted, and the Allies inflicted severe losses on the attacking troops, eventually destroying most of the German tanks involved in the attack. Although fighting continued around Mortain for six days, the American forces had regained the initiative within a day of the opening of the German attack.

As the German commanders on the spot had warned Hitler in vain, there was little chance of the attack succeeding, and the concentration of their armoured reserves at the western end of the front in Normandy soon led to disaster, as they were outflanked to their south and the front to their east collapsed, resulting in many of the German troops in Normandy being trapped in the Falaise Pocket.

On 25 July 1944, following six weeks of attritional warfare along a stalemated front, American forces under Lieutenant General Omar Bradley mounted an attack code-named Operation Cobra, which broke through the German defenses near Saint-Lô. Almost the entire western half of the German front in Normandy collapsed, and on 1 August, American forces captured Avranches. With the capture of this town at the base of the Cotentin peninsula, and an intact bridge at Pontaubault nearby, the American forces had "turned the corner"; the German front could no longer be anchored against the sea at its western end and American forces could advance west and south into Brittany. The U.S. Third Army, commanded by Lieutenant General George S. Patton, was activated the same day. Despite German air attacks against the bridge at Pontaubault, Patton pushed no less than seven divisions across it during the next three days, and units of his army began advancing almost unopposed towards the Brittany ports.

Beginning on 30 July, the British Second Army, under Lieutenant-General Miles C. Dempsey, mounted a supporting attack (code-named Operation Bluecoat) on the eastern flank of the American armies. Much of the German armored reserves being rushed west to halt the American breakthrough were diverted to face this new threat. Meanwhile, the U.S. continued its attacks to widen the corridor around Avranches. Although the Germans held the vital road junction of Vire, U.S. VII Corps, under Major General J. Lawton Collins, captured Mortain, 19 miles (31 km) east of Avranches, on 3 August.

The next day, although Major General Troy H. Middleton's U.S. VIII Corps continued to advance west through Brittany toward the ports of Brest and Lorient, Bradley ordered Patton to drive eastward with the main body of the U.S. Third Army, around the open German flank and into the German rear areas. Major General Wade H. Haislip's U.S. XV Corps advanced no less than 75 mi (121 km) during the next three days, and by 7 August they were approaching Le Mans, formerly the location of the headquarters of the German 7th Army, and still an important logistic center.

Generalfeldmarshall Günther von Kluge was the German supreme commander in the West. After Generalfeldmarschall Erwin Rommel was injured by Allied aircraft on 17 July, Kluge also took over direct command of Army Group B, the formation conducting the battle in Normandy. He had warned Hitler on 22 July that the collapse of the front was imminent, but Hitler continued to order him to stand fast.

On 2 August, Hitler, fearing the loss of U-boat pens on the French coast, sent a directive to Kluge ordering "an immediate counter-attack between Mortain and Avranches". General Walter Warlimont—the Deputy Chief of Staff at OKW, the German armed forces headquarters—was also sent to Kluge's headquarters to ensure these orders were complied with. Kluge suggested that there was no chance of success, and the German forces in Normandy should retire to the Seine River, pivoting on the intact defences south of Caen, but on 4 August, Hitler categorically ordered the attack to be launched. He demanded that eight of the nine Panzer Divisions in Normandy be used in the attack, and that the Luftwaffe commit its entire reserve, including 1,000 fighter aircraft. According to Hitler, three qualifications had to be met for the attack to proceed. "Von Kluge must believe in it. He must be able to detach enough armour from the main front in Normandy to create an effective striking force, and he must achieve surprise".