NEAR CORE CREEK, N. C., April 18, 1863-6.30 p. m.

Lieutenant-Colonel HOFFMAN:

COLONEL: My troops have been nearly all of them occupying positions in advance of Core Creek to-day, for the purpose of covering the operation of destroying the bridge at the Neuse-road Crossing.

I this moment learn the operation is successful, the enemy's pickets retiring at all quarters as our troops advance, we capturing but 4 cavalry soldiers, and orders have gone out to resume my position of last night in all respects. We have seen no indications of force to-day.

Very respectfully,

HENRY PRINCE.

I think they expect an advance on the railroad.

FORT MONROE, VA., April 19, 1863.

Major General H. W. HALLECK,

General-in-Chief:

The following dispatch is just received at 2.15 o'clock:

SUFFOLK, VA., April 19, 1863.

Major-General DIX:

Admiral Lee has ordered the boats out of the river. This is fatal. It must be stopped from Washington or elsewhere.

JOHN J. PECK,

Major-General.

Major-General Dix has gone to the Nansemond and is expected back at 5 p. m.

LOUIS H. PELOUZE.

SUFFOLK, VA., April 19, 1863.

Admiral S. P. LEE,

Newport News:

The withdrawal of all the boats above West Branch of the Nansemond at this crisis will be attended with great risk and may result in the enemy crossing. It will require me to detach many more regiments and guns, which I cannot afford. Earnest and continued co-operation of navy and army will best General Longstreet in this campaign, and I beg you to reconsider the proposition. For two or three [very] good cover is afforded, and other works are being constructed.

JOHN J. PECK,

Major-General.

UNITED STATES FLAG-SHIP MINNESOTA, Off Newport News, Va., April 19, 1863.

Major-General PECK,

Commanding at Suffolk, Va.:

Your telegraph is just received. Desire Lieutenant Lamson to await further orders from me. Our light draughts are much needed elsewhere. West Branch Battery should be taken or silenced.

S. P. LEE,

Actg. Rear-Admiral, Commanding N. Atlantic Blockading Squadron.