WASHINGTON — In an effort to secure Republican support for an overhaul of financial regulations, the chairman of the Senate Banking Committee on Monday proposed giving the Federal Reserve responsibility for protecting consumers from abusive and deceptive financial products.

The new plan, described by an official briefed on the negotiations, was the latest iteration of an idea that has divided members of the committee, largely along party lines, and has been the major barrier in the path toward the most significant overhaul of banking rules since the Depression, a priority of the Obama administration.

The chairman, Christopher J. Dodd, Democrat of Connecticut, circulated a proposal last week to create a Bureau of Financial Protection under the Treasury Department.

On Monday, the senior Republican on the committee, Richard C. Shelby of Alabama, having rejected that plan, put forward two of his own. One would create a consumer protection unit within the Federal Deposit Insurance Corporation, while the other would establish an interagency consumer protection council. In both cases, the new entity would have rule-making authority but limited enforcement powers.