Senate Republican Conference Chairman Lamar Alexander announced Friday that he will oppose the nomination of Solicitor General Elena Kagan to the Supreme Court.

The Tennessee lawmaker said he did not expect President Barack Obama to nominate a conservative-minded justice, noting that he voted for Obama’s last Supreme Court pick, Justice Sonia Sotomayor.

But he said he remains “deeply troubled by [Kagan’s] aggressive opposition to allowing military recruiters the same access to Harvard Law School as other prospective employers when she was its dean.” Alexander noted that he opposed Kagan’s nomination as solicitor general for the same reason.

Alexander said he is concerned that her track record at Harvard indicates she may be more inclined to “use her authority as a Supreme Court justice to advance her own policy preferences.”