President Obama announced plans Tuesday to bring high-speed Internet more quickly to the nation’s public schools, pledging to make sure students in the United States have every advantage that “some child in South Korea has right now.”

After all, Obama told a crowd at Buck Lodge Middle School in Adelphi, Md., “We shouldn’t give that kind of competitive advantage over to other countries.”

“In a country where we expect free Wi-Fi with our coffee,” he said, “we should definitely demand it in our schools.”

Obama made the remarks as he unveiled plans to speed up the phase-in of his pet ­project to link schools to the Internet through a combination of government investment and private-sector support. Several U.S. companies, including Apple, AT&T, Microsoft, Sprint and Verizon, are pitching in about $750 million in goods and services to help students get connected to the World Wide Web.

Along with an infusion of $2 billion from the Federal Communications Commission, the private money means an estimated 20 million students will get online access in their schools and libraries over the next two years. That is a quicker schedule than Obama anticipated when he launched this “ConnectED” initiative last year.

Back then, administration officials expected that the FCC would have to go through a lengthy rule-making process to free up $2 billion in a fund already dedicated to building capacity for high-speed Internet. But the FCC recently decided it could disburse the money more quickly, moving to speed up the funding of high-speed broadband projects without a commission vote.

The accelerated schedule comes without a single vote of Congress, Obama pointed out Tuesday, and “without adding a dime to the deficit.”

But he also warned lawmakers that he was about to ask them to pitch in.

He said he would ask Congress to “give teachers using cutting-edge technology the training they deserve” so that the technology the government is investing in can be used to its fullest.

The challenge showed Obama using his new second-term strategy, in which he announces a unilateral action by his administration and then urges Congress to make more sweeping change. In this case, he’s also rallying business leaders who have invested in these projects to bring their own voices to the call for congressional action.

“I’m going to ask every business leader to join us in this effort to give every young ­person every shot at success.”