WASHINGTON—Google Chief Executive Sundar Pichai plans to appear at a private meeting of top GOP lawmakers on Friday and again at a public hearing this year, responding to new scrutiny of the company’s work with China, its market power and alleged bias against conservatives in its search results.

The move comes amid growing regulatory concerns for the Alphabet Inc. unit and other big internet services such as Facebook Inc. and Twitter Inc., as bipartisan worries grow about the companies’ size and influence, as well as the potential for abuses.

“Google has a lot of questions to answer about reports of bias in its search results, violations of user privacy, anticompetitive behavior and business dealings with repressive regimes like China,” said House Majority Leader Kevin McCarthy (R., Calif.), who is organizing Friday’s meeting. He added that Mr. Pichai has “kindly” agreed to field Congress’s questions with Republican members on Friday. Mr. Pichai also is expected to appear at a House Judiciary Committee hearing after the November election.

Mr. McCarthy has complained that Google works with China to censor the internet but has canceled a contract with the U.S. military. Google this year said it wouldn’t renew a contract with the U.S. Department of Defense over employee concerns about aiding military projects; the company has also tested a mobile version of its search engine that would adhere to China’s strict controls over content, a person familiar with the matter said.

The tech industry began facing serious political challenges last year, amid revelations of Russian meddling in the 2016 election, but Google initially escaped some of the intense scrutiny that Facebook and Twitter have endured. Since then, however, the company has drawn fire over privacy on its Gmail service and allegations by conservatives that its search results stifle their viewpoints. Lawmakers have also expressed frustration with Google for not sending a top-level executive to a recent hearing.

“I look forward to meeting with members on both sides of the aisle, answering a wide range of questions, and explaining our approach. These meetings will continue Google’s long history of engaging with Congress, including testifying seven times to Congress this year,” Mr. Pichai said.

Mr. McCarthy, who is aiming to help preserve the GOP’s House majority and improve his chances of becoming speaker, has emerged as a vocal critic of the tech companies in recent months, as conservative voters appear to be focusing more on the issue of alleged political bias. He has been joined by President Trump, who recently accused Google of manipulating search results to highlight negative news reports about him.

Tech firms deny that they skew their news feeds, search or other functions to boost liberals or hurt conservatives.

Democrats including Sens. Mark Warner of Virginia and Elizabeth Warren of Massachusetts have also criticized Google on China and other issues.

Additional meetings planned for Washington this week could provide a glimpse of what steps policy makers and regulators could take to rein in the tech giants.

On Tuesday, U.S. Attorney General Jeff Sessions is expected to meet with state attorneys general to discuss alleged stifling of conservative speech online, as well as possible antitrust concerns over Google as well as Facebook and others. On Wednesday, the Senate Commerce Committee holds a hearing focused on internet privacy concerns, amid growing bipartisan calls for legislation to govern online data collection and use.

Tech firms also are facing a new documentary by a prominent conservative author, Peter Schweizer. The film, entitled “The Creepy Line,” raises allegations that tech firms hold too much power and suppress conservative views.

Conservatives’ current focus on big tech clearly has a potential political upside. A majority of Republicans—64%—say major tech companies support the views of liberals over conservatives, according to a recent Pew Research Center poll.

Allegations of anticonservative bias also could help divert attention from Russian meddling in the 2016 election that appeared to use tech platforms such as Facebook to manipulate public opinion and support Mr. Trump.

But the current antitech atmosphere goes beyond political maneuvering. As concerns grow among lawmakers and regulators, the debate appears to be expanding from politics to policy, and prospects for new regulation are increasing, no matter who wins the midterm election and control of the House and Senate.

That reality came home in a letter that a bipartisan group of senators wrote last week to the Trump administration, urging legislation to impose a new “enforceable nationwide standard” for collection and use of online data. The letter was written by the top Republicans and Democrats on two Senate Commerce subcommittees, Sens. Jerry Moran (R., Kan.), Roger Wicker (R., Miss.), Richard Blumenthal (D., Conn.) and Brian Schatz (D., Hawaii). The administration also could release its own set of principles for online privacy as soon as Tuesday. They could further fuel talk of broad online privacy legislation—something the tech companies have successfully avoided for years.

Write to John D. McKinnon at john.mckinnon@wsj.com and Douglas MacMillan at douglas.macmillan@wsj.com