JUNE 3, 1863. -Engagement near Simsport, La.

Report of Captain Henry Walke, u. S. Navy.

UNITED STATES GUNBOAT LA FAYETTE,

Red River,

June 3, 1863.

SIR: This morning I sent the Switzerland down to Simsport to make a reconnaissance, in compliance With your request of the 30th utlimo, and about three quarters of an hour after I heard a brisk firing in that vicinity, when I dispatched the Pittsburg, immediately for that place, but before she reached Atchafalaya the Switzerland met the Pittsburg and giving information of their engagement With two batteries of light guns and a considerable force of infantry, they both returned.

Colonel Ellet reports that four or five pieces of light artillery opened fire on him With about regiment of infantry wounding 3 of his men, 1 dangerously.

The Switzerland returned the fire passing below the batteries and also on her return; but not having the means of capturing the enemy or his guns, and his steam pipe disabled, he returned.

I have sent him to you for some troops, if they can be obtained so, that I can make an attack upon the enemy and capture his artillery and some of his troops, perhaps, by landing our troops immediately after driving them from their guns.

Colonel Ellet will report particulars.

In great haste, very respectfully, your obedient servant.

H. WALER,

CAPTAIN U. S. Navy.

Commodore JAMES S. PALMER,

Commanding Flag-ship Hartford.

JUNE - to 7, 1863. -Expedition from Jackson, Tenn., across Tennessee River.

Report of Major General Richard J. Oglesby, u. S. Army.

COLONEL: Lieutenant Colonel Breckenridge First WEST Tennessee Cavalry just returned to Jackson from expedition across Tennessee River. Destroyed a large amount of property, secured and put on gunboats there thousand sides of leather and recrossed without any loss, except stragglers.

Counts in to day-reports Chalmers at Panola week ago, With 1, 8000 infantry and one battery. Enemy all withdrawn from Mississippi swamps and encamped 14 miles below Yazoo City . On the 26th of May, Johnston had around Jackson 25,000. Reenforcements constantly arriving.

Three deserters confirm reports that but one brigade is a Port Hudson.

R. J. OGLESBEY,

Major-General.

Lieutenant-Colonel BINMORE,

Assistant Adjutant-General.