While the situation in Tobruk had become static warfare, there was much action in other theaters. 20 May 1941 had been the day that the Germans launched the airborne assault on the island of Crete. The Germans had secured their possession of Maleme airfield by 23 May. The next day, 24 May, the Bismarck sank the battle cruiser Hood in the Denmark Strait. The battle around Crete seriously depleted the British Mediterranean Fleet. By the end of May, the fighting in Crete had ended. About half of the men on Crete were evacuated. This was fairly soon after the debacle in Greece. With the German lack of commitment in Iraq allowed the hostile Rashid Ali to be forced from power. at this time, this was one of the few bright spots for the British.
In the Egyptian-Libyan frontier area, the Germans launched an attack on 26 May. The Germans had 160 tanks divided into four groups. They lacked sufficient fuel, so they were limited in what they could do. The British only had a small force at Halfaya Pass. They had 9 infantry tanks, some field guns, some anti-tank guns, and some anti-aircraft guns. The infantry were from the 3rd Coldstream Guards. The right group hooked towards Deir el Hamra. The center groups, heavy in tanks, was to go for Sidi Suleiman. The left group would go to the escarpment and would attack infantry.The German attack was successful, and the main result was to get a document from Churchill to the Chiefs of Staff.
Churchill thought that the Western Desert was the one venue where the British had the opportunity to launch a successful attack on the Germans. The Chiefs of Staff were sympathetic to Churchill's document, but wanted to get air power re-established in Cyrenaica. General Wavell responded by issuing orders for a new attack that he called Operation Battleaxe. The idea was that they would defeat the German forces at the Egyptian Frontier, and then break the enemy hold on Tobruk, and then move on to Derna and Mechili. The Australians in Tobruk were expected to be heavily involved. An ominous sign was that General Wavell warned the Chiefs of Staff that he felt that the chances of success were "doubtful".
There was a meeting in Cairo on 4 June. These were the Commanders-in-Chief and they talked about Tobruk in negative terms. Wavell's primary concern was that the enemy forces would launch a new attack on Tobruk (a "blitz"). Admiral Cunningham talked about the difficulties in keeping Tobruk supplied. Air Marshall Tedder remarked that there were few fighters to give support to Tobruk. This is based on the account in Vol.III of the Australian Official History.