WASHINGTON — It would be an unusual pairing, but two presidential hopefuls from opposite sides of the political spectrum, Senator Brownback and Senator Biden, could team up on a proposal for Iraq that splits the country into three loosely federated states.

Mr. Brownback, a Republican known for his social conservatism, suggested yesterday that the bipartisan proposal could follow President Bush’s veto this week of legislation tying war funding to a timetable for withdrawal of American troops. The Kansas senator voted against the Democratic bill, but he has occasionally veered away from his party’s base on the war, and he initially opposed the president’s decision to send more than 20,000 additional troops to Iraq earlier this year.

He has advocated a more aggressive diplomatic effort, and he even suggested yesterday, in an appearance on ABC’s “This Week,” that Secretary of State Rice should lead reconciliation talks among Sunni, Shiite, and Kurdish leaders in Iraq.

Like Mr. Biden, a Democrat of Delaware, Mr. Brownback is a long shot for his party’s nomination in 2008, but they share common ground in advocating a “three-state solution” in Iraq that sets them apart from their rivals on either side in the presidential campaign.

“I’ve reached out to Senator Biden. I’ve talked to him a couple of times about it,” Mr. Brownback said yesterday when asked about the possibility of working together on an Iraq proposal. “I think it is the only long-term, durable political solution for us to move forward. We can do it bipartisan. We can do it in the aftermath of this veto.”

Mr. Biden has made the proposal a centerpiece of his campaign, often criticizing his Democratic opponents for not offering their own plans for Iraq following the withdrawal of American combat troops. Under his plan, the country would be divided into three largely autonomous regions, which would be held together by a limited central government that would take responsibility for functions such as border security and the distribution of oil revenues.

The Iraqi Study Group considered the three-state solution as an alternative and rejected it, saying its potential costs were too high. Mr. Biden, appearing on NBC’s “Meet the Press” yesterday, defended the idea, citing the support of two former secretaries of state, Henry Kissinger and Madeline Albright.

He did not mention the possibility of teaming up with Mr. Brownback. His campaign referred questions to his Senate office. A spokeswoman, Elizabeth Alexander, said the two lawmakers had “talked briefly” about jointly proposing legislation, but she did not say whether a bill was in the offing.

The three-state proposal has not played a central role in the standoff between Congress and the White House over funding for the war and the insistence of Democrats to tie it to a timeline for American withdrawal. Ms. Rice yesterday indicated the president would not accept a softer version of a war funding bill that included benchmarks for the Iraqi government. Mr. Bush has invited congressional leaders to the White House to reopen negotiations once he vetoes the spending bill passed last week.

Mr. Biden, in a wide-ranging interview on “Meet the Press,” also assailed Mayor Giuliani for his comments last week that America would be less safe with a Democrat in the White House. He suggested that the Republican presidential candidate was directing his ire at the wrong person, criticizing the Bush administration for not supporting the implementation of security recommendations of the September 11 commission. “Rudy is being Rudy, and Rudy is dead wrong,” Mr. Biden said.

The Delaware lawmaker joins Senator Clinton and other leading Democrats, who attacked Mr. Giuliani last week over his remarks.