Despite a pledge to cut estate taxes by Independence Day, the Senate's Republican leader on Tuesday postponed action on a bill to reduce taxes for heirs.

Senate Majority Leader Bill Frist, R-Tenn., said he did not yet have enough votes to pass a bill, already approved by the House, that would eliminate taxes on the first $5 million of an individual's estate and cut taxes for others.

Most Republicans support the tax reduction, but they need support from a few more Democrats.

"The vast majority of my Democratic colleagues have so far refused to address this issue," Frist said in a statement. "It's my hope that their constituents will use the upcoming recess to explain the importance of supporting a reasonable and permanent solution to this unfair tax."

Senate Democratic leader Harry Reid of Nevada contended that Frist recognized that "the phony House 'compromise"' would be turned down by senators.

"The Senate has repeatedly rejected repeal of the estate tax because it recognized that giving away hundreds of billions in tax breaks to the wealthiest among us was the wrong priority for America," Reid said in a statement.

Frist lost one vote on the estate tax already this summer when opponents — most Democrats and a pair of Republicans — blocked debate on a bill repealing estate taxes after 2010.

Frist then turned to the House for help, asking GOP leaders for a bill that might attract enough support to pass this year, before a fall election with control of Congress at stake.

House tax-writers responded with a bill eliminating taxes for virtually all inherited estates, those worth up to $5 million for an individual and $10 million for a couple.

After those exemptions, estates worth up to $25 million would be taxed at rates equal to those on capital gains, currently 15 percent but scheduled to rise to 20 percent in 2011.

The remainder of any larger estates would be taxed at rates twice that of capital gains, or 30 percent at first and 40 percent when the scheduled capital gains tax increase takes effect.

The bill also would cut taxes for companies on certain timber gains.

The estate tax debate is made necessary because of a quirky law that eliminates the levy in 2010 but revives it a year later.

Frist said senators also must decide whether to make changes to the bill passed in the House. The House's most conservative Republicans have already signaled they could not accept any Senate attempt to negotiate for higher estate taxes.