HONG KONG — As Chinese companies try to snap up American tech businesses, they are setting off ripples of unease in the Obama administration and in Congress, inciting a backlash that has stopped the latest acquisition attempt.

One of the companies that first brought silicon to Silicon Valley — Fairchild Semiconductor International — said it would remain in American hands after rejecting a takeover offer worth about $2.5 billion led by Chinese state-backed buyers. Instead, Fairchild embraced a smaller bid from an American rival on Tuesday, citing concerns that federal regulators might reject the Chinese deal.

The unsuccessful Chinese bid for Fairchild was just one of at least 10 such offers in the last year for international semiconductor businesses, mostly in the United States. China’s Five-Year Plan, the government’s economic and strategic road map, has emphasized semiconductors as a core industry. And a long list of Chinese companies with varying ties to the government have been trying to acquire foreign technology in the sector.

Recent Chinese moves in areas like heavy equipment, aerospace and financial services are also drawing attention from both ends of the American political spectrum.

A group of 44 Republican members of Congress and one Democrat sent a letter on Tuesday afternoon to the Treasury Department, demanding that the Obama administration’s interagency committee on foreign acquisitions “conduct a full and rigorous investigation” of a bid by a company in Chongqing, China, to acquire the small but historic Chicago Stock Exchange.

Representative Robert Pittenger, Republican of North Carolina, said in a telephone interview that it had been easy to gather signatures on the letter in the House, with members worried that the deal would give China direct access to America’s financial infrastructure. “It took two days — generally, you’ll spend two weeks trying to get signatures,” he said.

But because semiconductors are the tiny electronic cores of a long list of military systems, including drones and smart bombs, Chinese interest in them has attracted the most attention in Washington. Those worries have been amplified as the Obama administration has repeatedly accused Beijing of cyberespionage against the United States. The worries have further increased as China has expanded its role in the South China Sea, including claims by the United States and Taiwan this week that China has deployed surface-to-air missiles there.

“China’s engaged in a buying spree of international semiconductor firms,” said Michael R. Wessel, a member of the United States-China Economic and Security Review Commission, a group created by Congress to monitor bilateral relations. “What they can’t develop on their own, they intend to buy, if they can, or steal, if they must.”

The Chinese government has vehemently denied that it is responsible for hacking attacks, while pointing to detailed disclosures by Edward Snowden of how the United States engages in extensive electronic intelligence gathering on China. Economists in China — and some in the United States, particularly at Wall Street banks that advise on Chinese acquisitions — argue that the United States needs to remain open to foreign investment, particularly given low American savings rates.

When Washington politicians start objecting to Chinese acquisitions, “they’re caught up by old-school, Cold War thinking,” said Fred Hu, a prominent Chinese economist and fund manager.

Fears about Chinese control over critical technologies recently prompted United States officials to block a $2.9 billion deal for Chinese investors to buy a controlling stake in a unit of the Dutch electronics company Philips.

Fairchild said in early January that it expected a bid from China Resources Microelectronics — a unit of the state-owned China Resources Holdings — and Hua Capital Management to be a “superior proposal.” That offer amounted to $21.70 a share in cash, compared with the $20 a share that ON Semiconductor, an American company, had on the table. But worries about the likelihood of approval from the Committee on Foreign Investment in the United States outweighed the attractiveness of the bid.

Fairchild’s decision shows the effect of broader political suspicion in the United States toward Chinese investment in the high-tech sector. Last summer, a similar but much larger deal was derailed before it even made it to regulators. The $23 billion bid for the American memory chip maker Micron by a Chinese state-controlled firm was undone by concerns about its political feasibility.

In that case, Senator Chuck Schumer, Democrat of New York, voiced worries about the deal’s effect on national security in a public letter to Treasury Secretary Jacob J. Lew. But Republicans are now starting to take up the issue, which means that it could take on a partisan dimension in an election year.

Despite the difficult climate, Chinese bids for American companies seem likely to increase, affected by a slowing Chinese economy and a desire by many Chinese companies to move money out of the country before China’s currency can weaken further against the dollar. In the sensitive microchip industry, deals are also being driven by more than $100 billion set aside by the Chinese government to help the country improve the sophistication and scale of the critical industry.

The number of deals involving a Chinese company that is trying to buy an overseas chip maker rose to 21 last year, including the offer for Fairchild, from eight in 2010, according to the data company Dealogic. There have already been five this year, worth $857 million.

That has drawn more attention to the Committee on Foreign Investment in the United States, also known as Cfius. An interagency body that includes representatives from the Treasury, Justice and Defense Departments, Cfius can recommend against foreign deals made for American companies, or companies connected to the United States, on grounds of national security. The agency can also broker compromises in which companies enact special security checks for sensitive aspects of an acquisition or sell off those assets.

Many in the semiconductor industry are watching closely to see whether Cfius will investigate a bid by the Chinese chip maker Tsinghua Holdings for a stake in the American company Western Digital, which makes hard disk drives. A lack of an investigation could herald more moves by Chinese investors to take minority stakes in American chip and memory companies.

The potential Chinese buyers of Fairchild had already agreed to pay a $108 million termination fee if the deal did not get approval from Cfius. They also increased their offer to $22 a share after Fairchild raised concerns. But Fairchild’s transaction committee said an agreement would still be too risky.

The Fairchild board said in a regulatory filing on Tuesday that it found the higher offer attractive but that there was “nonnegligible risk of a failure to obtain Cfius approval.”

Fairchild works on several technologies that could have raised concerns. In particular, it develops and produces sensors that track motion in three dimensions, which are used in many cutting-edge technologies. Xsens, a company acquired by Fairchild in 2014, works on sensors that guide unmanned submarines and drones and help in maritime surveillance.

Shares of ON Semiconductor closed up more than 6 percent on Tuesday, when Fairchild announced that it still favored the American company’s bid. Fairchild’s stock dropped almost 3 percent.