A coalition of online retailers backed by Amazon began a seven-figure advertising blitz on Wednesday opposing President Trump’s demand that the beleaguered United States Postal Service ratchet up its package delivery rates to avoid bankruptcy amid the coronavirus crisis, its top lobbyist said.

The coalition intends to spend more than $2 million on the campaign in an attempt to whip up Republican opposition to Mr. Trump’s idea, pressing lawmakers instead to support a multibillion-dollar rescue package proposed by Democrats that would help the Postal Service survive the sharp drop in revenue and mail volume caused by the pandemic.

The ads began running nationally Wednesday night on Fox News’s “Hannity” — one of Mr. Trump’s favorite programs — and will be featured on Rush Limbaugh’s radio show on Thursday. They do not mention the president, but label his proposal to jack up delivery prices by 400 percent “a massive package tax” on small businesses and Americans who rely on the mail for prescription drugs and other goods.

Amazon, CVS and others involved in the campaign rely on the Postal Service for delivery of millions of packages a year and could see significant business disruptions if the agency had to sharply increase rates or went bankrupt.

Many of the companies have been quietly lobbying lawmakers on Capitol Hill on the issue, but the advertising push will more visibly establish their position in a high-stakes political fight over the Postal Service’s finances and future. Democrats have been pressing to include $25 billion in the next round of coronavirus relief legislation to prop up the service, which has said it could run out of cash by September without a lifeline from Congress.

But Mr. Trump has said he will not sign any pandemic relief package that helps the Postal Service unless it raises its rates. His views on the service appear to be predominantly shaped by his antipathy toward Amazon’s founder, Jeff Bezos, who also owns The Washington Post.

“All of these companies know that in order to keep that market competitive and to keep operations most efficient, an affordable U.S.P.S. involvement is absolutely essential,” said John M. McHugh, the former Army secretary and the coalition’s chairman. He called Mr. Trump’s proposal “dangerous,” particularly at a time when Americans sequestered at home are increasingly reliant on delivery services and postal leaders are projecting yawning deficits.

Democrats have already endorsed an April request by the Postal Service’s board of governors for more than $25 billion in emergency funds and other debt relief measures to get the service through the crisis. If Republicans in Congress lent their support, as well, it could increase pressure on Mr. Trump to go along.

On Wednesday, Representative Steny H. Hoyer, Democrat of Maryland and the majority leader, called the agency a “connective organ of our society” that Democrats would not allow to fail.

“We believe that we have to make sure the Postal Service, which is at risk of going bankrupt, will not,” he told reporters.

Republican and Democratic lawmakers had reached a tentative agreement during negotiations on the coronavirus stimulus package to send the Postal Service direct cash, but Mr. Trump and Steven Mnuchin, the Treasury secretary, nixed the funds in favor of loan authority that allows the Treasury Department to set terms forcing the agency to raise prices and make other changes that would reduce costs and potentially disrupt service standards.

Small-government conservatives have long advocated shrinking the Postal Service, one of the federal government’s largest agencies with a well-paid, unionized work force, to allow private delivery services like FedEx and UPS to gain greater market share. And many Democrats agreed that the agency’s business model before the pandemic was not sustainable. But Mr. Trump’s dim view of the agency appears to be more personal.

The president has said repeatedly that he believes the Postal Service is undercharging Amazon to deliver small packages. Aides say Mr. Trump has fixated on the company because of Mr. Bezos’s ownership of The Post, whose news coverage and editorial opinions the president frequently attacks.

The president has called the Postal Service Amazon’s “delivery boy” and called the national mail system “a joke” because of its dealings with the company.

More recently, Mr. Trump said, incorrectly, that the agency lost money on each package it delivered for Amazon and other online retailers. Independent analysts also say that a rate increase as significant as the one Mr. Trump wants would probably backfire, driving away customers for the Postal Service and leaving it in a weaker financial position.

“For whatever reason, you can imagine, they don’t want to insult Amazon and these other groups,” Mr. Trump said in the Oval Office in late April. “If they don’t raise the price, I’m not signing anything.”

Mr. McHugh said the concerns of his group, called the Package Coalition, were larger than Amazon.

“We are not looking for a fistfight with the president,” Mr. McHugh said, but he added that Mr. Trump’s antipathy toward Amazon has been clear.