The shareholder votes would not be binding on company management.

The measure tries to reduce the potential conflicts of interest involving compensation consultants who play a central role in blessing pay packages. Many of those consultants also provide other services to the companies, putting them in a conflicting role for issuing fairness opinions about pay.

Image Representative Barney Frank, right, the Democratic chairman of the House Financial Services Committee, and Representative Spencer T. Bachus III, the ranking Republican member. Credit... Pablo Martinez Monsivais/Associated Press

The measure also gives regulators the authority to prohibit inappropriate or risky compensation practices for banks and other regulated financial institutions.

The Senate is not expected to consider the legislation until this fall, at the earliest.

The Obama administration’s executive pay proposal, embodied in legislation sponsored by Representative Barney Frank, Democrat of Massachusetts, is part of its larger package of regulatory changes intended to reduce the chances of another economic crisis.

While the measure still faces political obstacles in the Senate, it has not encountered as much resistance as two other cornerstones of the administration’s proposal  a greater role for the Federal Reserve in monitoring large institutions that could pose risks to the financial system and the creation of a new agency to protect consumers from deceptive or ill-suited mortgages, credit cards and other kinds of loans.

The legislation comes as the Obama administration is separately examining the pay practices of seven big companies that have received significant taxpayer assistance in recent months. The administration’s top official for compensation, Kenneth R. Feinberg, has been in discussions with the companies as he considers whether to approve the compensation of top executives at American International Group, Citigroup, Bank of America, General Motors, Chrysler and the financing arms of those two automakers.