WASHINGTON—The nation’s biggest business lobbying group and a national tax-services firm both sued the Federal Trade Commission on Wednesday, igniting a flare of lawsuits over the agency’s regulation aimed at ending noncompete agreements.

The U.S. Chamber of Commerce challenged the regulation in federal court in East Texas, while the tax firm Ryan LLC filed its lawsuit in Dallas. Other business groups joined the chamber’s suit, including the Business Roundtable, which represents chief executive officers of some of the country’s biggest employers.

Noncompete clauses violate a 110-year-old law that prohibits unfair methods of competition, the FTC says. The restrictions hamper competition for labor, the agency says, because employees can’t easily leave for higher pay and better benefits. Removing them would boost employee earnings by $400 billion or more over 10 years, the FTC estimates.

The Chamber’s lawsuit says policymakers and courts have for decades recognized the value of noncompete agreements, while state governments have put curbs on them “when they go too far.” The federal government has never regulated noncompete contracts, the Chamber says, and Congress never authorized the FTC to step in and take over for the states.

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