Jump bikes will be available through Uber’s app. Jump is one of five dockless bike-share operators in the District. (Brendan Smialowski/AFP/Getty Images)

The messy battle for the future of urban transportation is playing out in the gridlocked and bike-cluttered streets and sidewalks of the District — and the subway tunnels underneath it.

On Wednesday, Uber chief executive Dara Khosrowshahi appeared in Washington with Mayor Muriel E. Bowser (D) to announce a suite of new initiatives aimed at positioning the ride-hailing app as a one-stop shop for urban mobility. The company is expanding its business to include bike-share, car rental and eventually transit, which customers will be able to access and pay for within its all-purpose app. The District is the testing ground for several of the company’s projects.

But in heralding the company’s partnership with the city, Khosrowshahi also used the opportunity to subtly criticize Bowser’s proposal to tax ride-hailing companies, including Uber, to raise money for the city’s share of the Metro funding package.

“What we want to make sure is that you’re not taxing one form of shared transportation for another form of shared transportation,” Khosrowshahi said. “We are in this to promote shared transportation in general. We want to make sure that proposals like this are not unconstructive to that goal.”

Bowser has proposed raising ride-hailing companies’ gross receipts tax to 4.75 percent from 1 percent to pay for about 10 percent of the $178.5 million that represents the District’s portion of $500 million in annual dedicated funding for Metro. The transit agency is struggling amid chronic safety and reliability issues, and it has faced falling ridership as a result, as well as increased competition from Uber, Lyft and other services.

City officials say the services have benefited from Metro’s problems so it’s only fair they be a part of the solution.

Chicago Mayor Rahm Emanuel (D) used a similar approach when he levied a 15-cent additional fee on ride-hailing trips to fund a Chicago Transit Authority modernization plan. But the D.C. fee increase, which would translate to about 37 cents more on a $10 trip if Uber decides to pass it on to customers, is higher than in other cities.

Bowser noted that the ride-hail tax is one piece of a plan that also raises sales and commercial property taxes, while pulling savings from elsewhere in the city budget.

“The benefits of Metro serve all of us,” she said. “That is the package that we think is the most fair — that hits property owners, it hits visitors, it hits residents and it hits the ride-sharing services — that we think is best for the city.”

Khosrowshahi said Uber supports dedicated funding for Metro, seeing it as a proposal “that ultimately, long term, is going to benefit us as well.”

He joined Bowser for a policy discussion Wednesday on the “Future of Mobility” that was held at Uber’s driver-support hub in Northeast Washington.

In his comments on the panel, Khosrowshahi described how proposals such as Bowser’s could affect start-ups, which rely on large sums of venture capital to subsidize their fares, by hampering their growth.

He noted how Uber, for example, invests hundreds of millions to offer deeply discounted shared-ride services such as UberPool and Express Pool.

“We are having to discount very aggressively, much more so than you would think, shared ride and Express Pool rides to get people to want to try this new mode of transportation,” Khosrowshahi said. “It requires sustained investment, it requires big investments, and it’s something we’re very much behind.”

“When you think about the transit [proposals],” he added, “you don’t want to be taxing one kind of shared mobility to help another.”

On Monday, Uber announced its purchase of Jump Bikes, a dockless e-bike service that operates in the District and San Francisco. Jump is one of five dockless bike-share operators in the city, and the District often is among the first places mobility start-ups launch in the United States.

With Jump’s integration into the Uber app, users can reserve, unlock and pay for the bikes the same way they’d hail a ride. Uber said it also intends to double the number of bikes in the city to 400 — the maximum allowed under the District’s dockless bike-share pilot.

The company also announced Wednesday that it will partner with car-sharing app Getaround to offer car rentals for riders and drivers. That service will be offered beginning later this month — but only in San Francisco for now, Uber said. Getaround lets users rent private cars from their owners — often at costs cheaper than car-rental companies — and allows owners to make money on their vehicles when they aren’t using them.

And in another example of how the company is fashioning itself into an all-inclusive app, it announced a partnership with the transit ticketing service Masabi. Through the deal, Uber users will be able to pay for transit rides in its app or scan into rail and bus services using their smartphones. The service will also include integration of transit maps and schedule information in selected cities. Despite an upcoming upgrade that will allow Metro riders to pay fares using their smartphones, the Washington Metropolitan Area Transit Authority is not one of the systems involved, Uber said.

“It is somewhat compelling to be able to get all your transportation through one platform,” said Jahan Khanna, Uber’s head of product for mobility. “Uber is going to invest more specifically in modes that are not just ride-hailing.”

It’s part of the company’s larger vision.

“Imagine there’s a car-sharing network that has cars every half a mile,” Khanna said. “Now you can take a bike to rent your car and go buy groceries.”

(Washington Post owner Jeffrey P. Bezos was an early investor in Uber.)