EXECUTIVE DEPARTMENT, Las Vegas, N. Mex., April 13, 1862.

W. H. SEWARD, Secretary of State:

SIR: I have the honor to inform the Department that on the 11th instant Colonel Canby formed a junction with the command under Colonel Paul at Gallisteo, 15 miles south of Santa Fe,and proceeded by forced marches on to Albuquerque, at which place the enemy with their entire force had concentrated. On his march upwards and in the town or neighborhood of Albuquerque Colonel Canby had an encounter with either the whole or a part of the enemy's forces, in which it is said he took several pieces of artillery, and that Major Duncan, of our cavalry, was wounded in the head.

Colonel Canby made the detour by way the Canon Carneval, and came on the east side of the mountains to the junction at Gallisteo. To-day he will arrive at Albuquerque, and doubtless decide the question of the occupancy of this Territory by the Texans. It is thought the Texans are in hasty retreat,and have full three days' march the advantage. Should that be the case,will not be easy to overtake them. Colonel Kit Carson, with his entire regiment,and some auxiliary forces, is still at Craig, and may officer some embarrassment to the safe retreat of the enemy.

I think there can be no doubt as to the result of any action between the forces under Colonel Canby, now united with the late victorious troops from Denver, and the enemy, with all the forces they have in the Territory.

The cavalry and means of transportation on both sides are completely broken down, and neither a retreat nor pursuit can be effected with any degree of rapidity.

The Territory has been completely exhausted of grain on the route of the military movements, and nothing can be obtained of forage for animals.

I give you herein the latest news from and the positions of the different forces. Not having left for the capital the day mentioned in my last, of the 10th instant,has enabled me to do so. I leave on to-morrow for that place,and will by next mail give you the result of the impending conflict.

I am, sir, very respectfully, your obedient servant,

HENRY CONNELLY,

Governor of New Mexico.

P. S.-The inclosed communication from Colonel Paul was received after the above was written. I forward it for the satisfaction of the Department.

[Copy furnished War Department by Secretary of State May 6, 1862.]

[Inclosure.]

HEADQUARTERS EASTERN DISTRICT, Gallisteo, N. Mex., April 12, 1862.

His Excellency HENRY CONNELLY,
Governor of New Mexico, Las Vegas, N. Mex.:

SIR: It affords me great pleasure to inform you that Santa Fe is now in our possession, and that You Excellency will hazard nothing by returning to the seat of government and resuming the duties of your office whenever it may suit your convenience.