HEADQUARTERS ARMY OF NORTHERN VIRGINIA, May 6, 1863. MAJOR-GEN. J. HOOKER, Commanding Army of the Potomac. General,--I have had the honor to receive your letter of yesterday, requesting permission to send a burial-party to attend to your dead and wounded on the battle-field of Chancellorsville. I regret that their position is such, being immediately within our lines, that the necessities of war forbid my compliance with your request, which, under other circumstances, it would give me pleasure to grant. I will accord to your dead and wounded the same attention which I bestow upon my own; but, if there is any thing which your medical director here requires which we cannot provide, he shall have my permission to receive from you such medical supplies as you may think proper to furnish. Consideration for your wounded prompts me to add, that, from what I learn, their comfort would be greatly promoted by additional medical attendance and medical supplies. I have the honor to be, Respectfully, your obedient servant, R. E. LEE, General. HEADQUARTERS ARMY OF THE POTOMAC, May 6, 1863, 4.30 P.M. HIS EXCELLENCY A. LINCOLN, President of the United States. Have this moment returned to camp. On my way received your telegrams of eleven A.M. and 12.30. The army had previously re-crossed the river, and was on its return to camp. As it had none of its trains of supplies with it, I deemed this advisable. Above, I saw no way of giving the enemy a general battle with the prospect of success which I desire. Not to exceed three corps, all told, of my troops have been engaged. For the whole to go in, there is a better place nearer at hand. Will write you at length to-night. Am glad to hear that a portion of the cavalry have at length turned up. One portion did nothing. JOSEPH HOOKER, Major-General. EXECUTIVE MANSION, WASHINGTON, D. C., May 7, 1863. MAJOR-GEN. HOOKER. My dear Sir,--The recent movement of your army is ended without effecting its object, except, perhaps, some important breakings of the enemy's communications. What next? If possible I would be very glad of another movement early enough to give us some benefit from the fact of the enemy's communication being broken; but neither for this reason or any other do I wish any thing done in desperation or rashness. An early movement would also help to supersede the bad moral effect of the recent one, which is said to be considerably injurious. Have you already in your mind a plan wholly or partially formed? If you have, prosecute it without interference from me. If you have not, please inform me, so that I, incompetent as I may be, can try and assist in the formation of some plan for the army.