_PETROGRAD, June 3.--Petrograd admits the loss of the fortress in the following official bulletin:_ As Przemysl, in view of the state of its artillery and its works, which were destroyed by the Austrians before their capitulation, was recognized as incapable of defending itself, its maintenance in our hands only served our purpose until such time as our possession of positions surrounding the town on the northwest facilitated our operations on the San. The enemy having captured Jaroslau and Radymno and begun to spread along the right bank of the river, the maintenance of these positions forced our troops to fight on an unequal and very difficult front, increasing it by thirty-five versts, (about twenty-four miles,) and subjecting the troops occupying these positions to the concentrated fire of the enemy's numerous guns. Przemysl was bombarded with heavy guns up to 16-inch calibre, and the enemy delivered his principal attack against the north front in the region of Forts 10 and 11, which the Austrians had almost completely demolished before the surrender of the fortress. When we repulsed these attacks the enemy succeeded in taking several of our guns, which had bombarded the enemy's columns until the latter were close to the muzzles, and the last shell was spent. According to supplementary information we took two hundred prisoners and eight quick-firers. In Galicia on Monday between the Vistula and Przemysl stubborn fighting developed, our troops gaining somewhat important successes on the left bank of the lower San, taking several villages, some with the bayonet. On the right bank of the same river we were successful near the village of Kalukouve, taking a base south of the village, capturing 1,200 prisoners, including twenty-two officers and eight quick-firers. RUSSIAN RETREAT FROM PRZEMYSL. _VIENNA, (via London,) June 4.--The Austrian War Office this evening issued the following official communication announcing the retreat of the Russians from Przemysl, their stand at Medyka, ten miles to the east, and their defeat at other points:_ During the day Przemysl was cleared of the enemy, who is retreating in an easterly direction, offering resistance on the height southwest of Medyka. The allied troops there are attacking. Meanwhile the army of the Austrian General Eduard von Boehm-Ermolli has succeeded in breaking through the Russian defensive positions from the south, and advanced in the direction of Mosciska, on the railroad to Lemberg, ten miles beyond Medyka, within a short distance of which our troops now hold positions. In these engagements we have captured numerous prisoners. The army under General Alexander Linsingen also has achieved fresh successes, and the Russians are in full retreat before him. On the Pruth line, in consequence of the events on the San and the upper Dniester, further fighting has developed. Wherever the enemy attempts an attack he is repulsed with severe losses. We have captured 900 men.