It was a U.S. Congress that did that. In the House the vote was 60 for and 49 against. Virtually none of the votes in favor of the end of slave imports came from representatives from slave-holding states. In the Senate the vote was 18 to 8. Many Southern senators didn't vote on the measure, possibly in protest. It might be more accurate to say that slave imports were ended in spite of Southern leaders rather than because of them.
The end of the slave trade was part of the bargain struck in 1787. Virginia did not want it to continue. They had more slaves than they needed, and wanted to sell them to the Deep South.