The Senate has rejected a bill designed to cut inheritance taxes on multimillion-dollar estates.

Republicans had proposed the bill to increase the federal estate tax exemption to $5 million per person and reduce the amount taxed on larger estates. In an attempt to sway Senate Democrats, GOP lawmakers had linked the tax cuts to a popular measure to increase the federal minimum wage.

The bill, however, failed in a 56-42 vote. Senate Majority Leader Bill Frist (R-Tenn.) says the bill will come up for debate again this fall.

The House passed a version of the bill on July 29.

—Tim Chan