WASHINGTON — The Supreme Court on Monday agreed to decide whether the father of a Marine killed in Iraq may sue protesters who picketed his son’s funeral with signs that read “God Hates You” and “Thank God for Dead Soldiers.”

A federal appeals court dismissed the suit on First Amendment grounds and threw out a $5 million award against the protesters, who are members of Westboro Baptist Church in Topeka, Kan., and maintain that God hates homosexuality and that the death of soldiers in Iraq and Afghanistan is God’s way of punishing the United States for its tolerance of it.

The fallen Marine was Lance Cpl. Matthew A. Snyder, and his funeral was held in Westminster, Md., in 2006. His father, Albert Snyder, testified at trial in 2007 that the protests continued to haunt and disturb him.

“For the rest of my life,” Mr. Snyder said, “I will remember what they did to me, and it has tarnished the memory of my son’s last hour on earth.”