“To protect millions of small businesses and the American farmer, we are finally ending the crushing, the horrible, the unfair estate tax, or as it is often referred to, the death tax,” Mr. Trump said.

Estates are taxed at a rate of 40 percent, but the first $5.49 million of an inheritance is exempt from taxation. Couples can leave their heirs as much as $11 million, none of it taxed, meaning only a few thousand wealthy estates are subject to the tax a year.

Preliminary analyses of the tax framework produced by the “Big Six” Republican tax working group last month were faulted for overwhelmingly benefiting the rich while potentially increasing taxes on some upper-middle-class families. The overall cost of the plan is expected to add $1.5 trillion to the deficit and, according to the Tax Policy Center, repealing the estate tax would reduce federal revenues by $239 billion over a decade.

Mr. Mnuchin expressed confidence on Friday that tax legislation would at least “break even” and that it would likely reduce the deficit because of the robust economic growth he thinks it will create. However, he said that because of congressional rules about calculating the effects of the tax bill on the economy, some of the changes to the tax code will likely have to expire.

“Parts will be permanent and parts will be temporary,” Mr. Mnuchin said.

The Tax Policy Center estimates that 11,310 people will die this year who leave estates large enough that their heirs will need to file estate tax returns and that two-thirds of these estates will be in the top 10 percent of income earners. Just 80 small farms and closely held businesses are expected to pay an estate tax in 2017, the center, a right-leaning think tank, projected.