WASHINGTON — Mayor Bloomberg is siding strongly with the Paterson administration and against three New York lawmakers in the debate over whether Albany can tax out-of-state companies who do business in New York.

Seeking millions in added tax revenues, the administration this spring enacted a pair of provisions to assess business taxes against out-of-state banks that issue credit cards in New York and to force online retailers such as Amazon.com to collect state and local sales taxes on goods shipped to the state. Those changes could be undercut by a federal bill backed by Senator Schumer and Reps. Anthony Weiner and Gregory Meeks that would restrict the ability of states to collect taxes from companies with no “physical presence” in the state.

Weighing in on the issue yesterday, the mayor said it was a matter of fairness for a Web site such as Amazon.com to pay the same tax rate as a local bookstore.

“If you are going to have a tax system, one of the essences of it should be that it is fair,” Mr. Bloomberg told reporters, responding to an article in yesterday’s New York Sun. “And it just inherently makes no sense whatsoever to tax you if you want to buy a book from Amazon differently than if you want to buy a book from a bookstore. I’d feel the same way about the food vendor with the cart outside or the coffee vendors. They should be paying the same kind of sales taxes as somebody who rents a store and sells coffee from that store.”

The mayor said it “probably wasn’t the worst idea” for governments to extend a tax break to online retailers when the Internet was “in its infancy.” Now that online shopping has more than caught up with traditional sales, the tax rates should be the same, he said.

Amazon.com is suing New York State over the new requirement, arguing it violates the Commerce Clause of the Constitution. Supporters of the federal bill say it was not intended to affect the New York sales tax law, but a tax expert told the Sun that the pending court case could bring the two measures into conflict.

Mr. Bloomberg was in Washington to testify before the House Committee on Education and Labor. Appearing alongside the schools chancellor, Joel Klein, he touted the city’s effort to overhaul its education system during his tenure, and boasted of the dramatic rise in test scores over the last year. He urged lawmakers to demand accountability from school districts as they make funding decisions, saying Congress should use the “power of the purse” to punish jurisdictions that “fail to take meaningful steps toward reform.”

The mayor later held a private meeting with Senator Clinton, during which he invited the former first lady to a “welcome back” event in New York City to celebrate her historic presidential run. A City Hall spokesman, Stuart Loeser, said the event would be at Gracie Mansion, but that neither a date nor a guest list had been set.

The two leaders often praise each other in public, although for a period last fall it looked as if they might face off as part of a three-candidate presidential race.

Mr. Bloomberg and Mrs. Clinton were initially mum on what came up during the more than 15-minute meeting that followed a presentation by the mayor to the Senate Democrats’ weekly policy lunch. “The American League versus the National League,” Mr. Bloomberg quipped, referring to the 15-inning All-Star Game that he attended Tuesday at Yankee Stadium.

Mrs. Clinton said they discussed priorities for the city, chiefly the New York delegation’s effort to secure funding for health programs for ground zero recovery workers who have illnesses linked to the aftermath of the September 11, 2001, terrorist attacks.