WASHINGTON—Prosecutors are gathering evidence for a grand-jury probe into whether congressional staff helped tip Wall Street traders to a change in health-care policy, an indication the long-running investigation has entered a more serious phase.

Public documents show federal law-enforcement officials and the Securities and Exchange Commission are seeking records and other evidence from the House Ways and Means Committee and a top congressional health-care aide, Brian Sutter, staff director of the committee's health-care subpanel.

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