“We want to continue to support the wonderful people, businesses and communities we have come to love in the Peach State,” according to the letter, which was dated Thursday and addressed to the governor and the speaker of the House of Representatives. “But we will not do so silently, and we will do everything in our power to move our industry to a safer state for women if H.B. 481 becomes law.”

The American Civil Liberties Union also promised to go to court if the bill becomes law.

“For 50 years the Supreme Court has said that banning abortions before the point of viability is unconstitutional,” Sean J. Young, the legal director of the A.C.L.U. of Georgia, said on Saturday. “Every judge that has heard a challenge to such abortion bans has struck them down.”

A spokesman for Mr. Kemp could not be reached on Saturday. The governor campaigned on a promise to sign tough abortion laws and said he welcomed the chance to “fight for life at the Capitol and in the courtroom.” On Friday, he praised lawmakers for their leadership and courage.

“We stand up for the innocent and speak for those who cannot speak for themselves,” he said on Twitter. “The legislature’s bold action reaffirms our priorities and who we are as a state.”

The bill would effectively change the limit on abortion in Georgia to six weeks from 20 weeks. The measure allows exceptions to prevent death or serious harm to the woman, in cases in which the pregnancy is “medically futile” because the fetus would not be able to live after birth, and in cases of rape or incest in which a police report has been filed.

Genevieve Wilson, a spokeswoman for Georgia Right to Life, said the group supported the measure until exceptions were added.

“While H.B. 481 contains some strong personhood components, such as declaring babies in the womb natural persons, we are very saddened that it also denies equal justice and equal protection for subclasses of children in the womb,” she said on Saturday.