Prior to the Civil War, the radical fringe of the pro-slavery movement was pushing for re-opening of the trans-Atlantic slave trade, banned under federal law since 1808. Davis, and most pro-slavery leaders opposed this effort. When Davis was attacked by Southern firebrands prior to the War for his opposition to a renewed international slave trade, Davis stated that his concern was for the well-being of Mississippi, a state with a large slave population, rather than abolitionist concern over the well-being of slaves.
The Confederate Constitution banned the international slave trade, except with the United States:
(1) The importation of negroes of the African race from any foreign country other than the slaveholding States or Territories of the United States of America, is hereby forbidden; and Congress is required to pass such laws as shall effectually prevent the same.
The issue came up quite early in the term of Davis as President of the CSA, when he vetoed a measure in regard to the international slave trade.
VETO MESSAGE.
EXECUTIVE DEPARTMENT, February 28, 1861.
Gentlemen of Congress: With sincere deference to the judgment of Congress, I have carefully considered the bill in relation to the slave trade, and to punish persons offending therein, but have not been able to approve it, and therefore do return it with a statement of my objections. The Constitution (section 7, article I.) provides that the importation of African negroes from any foreign country other than slave-holding States of the United States is hereby forbidden, and Congress is required to pass such laws as shall effectually prevent the same. The rule herein given is emphatic, and distinctly directs the legislation which shall effectually prevent the importation of African negroes. The bill before me denounces as high misdemeanor the importation of African negroes or other persons of color, either to be sold as slaves or to be held to service or labor, affixing heavy, degrading penalties on the act, if done with such intent. To that extent it accords with the requirements of the Constitution, but in the sixth section of the bill provision is made for the transfer of persons who may have been illegally imported into the Confederate States to the custody of foreign States or societies, upon condition of deportation and future freedom, and if the proposition thus to surrender them shall not be accepted, it is then made the duty of the President to cause said negroes to be sold at public outcry to the highest bidder in any one of the States where such sale shall not be inconsistent with the laws thereof. This provision seems to me to be in opposition to the policy declared in the Constitution – the prohibition of the importation of African negroes – and in derogation of its mandate to legislate for the effectuation of that object. Wherefore the bill is returned to you for your further consideration, and, together with the objections, most respectfully submitted.
JEFF’N DAVIS.
An attempt to override the veto was attempted in the Confederate Congress and failed.
Donald R. McClarey
Paul Zummo
Almost Chosen People 
I’m not sure what the purpose of this post is — the sole reason for the South’s ban on more imported slaves, they had far too many, and were terrified already of the hyperabundance of slaves.
In fact, the govenor of Georgia spoke openly about having to kill the slaves, rather than free them, because there were so many. The governor of Florida declared that Lincoln, just by opposing the SPREAD of slavery, was “like burning us to death slowly” because of the hyper abundance of slaves.
In fact the over abundance, and fantastic birth rate, of slaves, was the primary pressure cooker for the South’s frantic effort to SPREAD slavery. As Toombs declared, “Expand or Perish.”
Notice the first Ultimatum issued by the Confederacy, its leaders still in Montgomery in March of 61, was for the violent SPREAD of slavery, against the expressed and overwhelming wishes of the people in the territories.
No, you are quite wrong on that. There was a vocal movement among some extreme elements of the pro-slavery forces prior to the Civil War to re-open the slave trade.
http://abolition.nypl.org/print/revival_of_slave_trade/
As the sky-rocketing prices of slaves in the Cotton South indicated, there was a shortage of slaves on those plantations.
Different parts of the South had different economic stakes in a revival of the slave trade, just as the economic stakes of established planters like Jefferson Davis, differed from new planters who wanted cheap slaves.