The Democratic National Committee sued the Russian government, the Trump campaign and WikiLeaks on Friday, accusing them of a wide-ranging conspiracy to interfere in the 2016 presidential election to defeat Democrat Hillary Clinton.

The lawsuit alleges the defendants conspired before the election to hack into the DNC’s computer network and strategically leak the stolen information to bolster Donald Trump’s chances of winning the election. The conspiracy sought to undermine Mrs. Clinton’s campaign because Mr. Trump’s presidency was expected to benefit Russian political and financial interests, which would, in turn, benefit Mr. Trump’s financial interests, the lawsuit alleged.

The DNC accused the Trump campaign of having “repeated secretive communications” with Russian agents and WikiLeaks.

“We’re taking this action because we believe no one is above the law, and we must pursue every avenue of justice against those who engaged in this illegal activity against the DNC and our democracy,” the committee said in a statement.

Among the lead defendants in the lawsuit are the Russian Federation and Russia’s military intelligence agency, as well as WikiLeaks and its founder, Julian Assange.

The lawsuit doesn’t name Mr. Trump as a defendant, but it names individuals either currently or previously in his inner circle, including Donald Trump Jr., his son-in-law and White House adviser Jared Kushner, longtime adviser Roger Stone and former campaign chairman Paul Manafort.

“Just heard the Campaign was sued by the Obstructionist Democrats,” wrote Mr. Trump in a tweet Friday afternoon. Mr. Trump said it “could be good news“ and pledged to countersue to get “the DNC Server that they refused to give to the FBI, the Debbie Wasserman Schultz Servers and Documents held by the Pakistani mystery man and Clinton Emails.”

In a statement, the Trump campaign said the lawsuit is “frivolous” and “without merit,” calling it “a last-ditch effort to substantiate the baseless Russian collusion allegations.”

The Trump campaign said that if the lawsuit proceeds, it would “leverage” the discovery process to probe the DNC’s own records related to the 2016 election.

None of the other defendants responded to requests for comment. Russia has denied having meddled in the election, and the Trump campaign has denied having worked with the Russians.

The lawsuit, filed in federal court in Manhattan, the home base of the Trump campaign, seeks an unspecified amount of damages and requests a jury trial. The DNC said in the suit it paid more than $1 million in the fallout of the hack to repair electronic equipment and hire additional staff. One DNC official estimated the organization may have suffered “hundreds of millions of dollars” in overall damages from the breach.

DNC Chairman Tom Perez has been interested in a legal remedy to the hack since his election as chairman in February 2017, according to the DNC official, and the organization had been gathering facts and finding the right law firm to support a lawsuit. The DNC is represented by law firm Cohen Milstein Sellers & Toll PLLC, which is also representing victims of the 2015 breach into health insurer Anthem Inc.

The email disclosures after the hack had a “chilling effect” on donations to the DNC and resulted in “substantial loss of income” to the organization, according to the DNC. The lawsuit said the organization’s employees were exposed to harassment and death threats as a result of the leaked emails.

Special counsel Robert Mueller has publicly charged a total of 19 people in a wide-ranging probe into what U.S. intelligence officials say was a Russian campaign designed to influence the 2016 election and help Mr. Trump win. Three Trump associates have pleaded guilty to criminal misconduct and have agreed to cooperate in the investigation.

Mr. Manafort and business partner Richard Gates were charged with financial crimes and lobbying work unrelated to the Trump campaign. Mr. Manafort has pleaded not guilty; Mr. Gates struck a plea deal in late February.

Mr. Mueller’s probe hasn’t spawned charges related to the DNC hack, which was detected by the organization in April 2016. In February, federal prosecutors indicted three Russian companies and 13 Russian citizens for election meddling related to social media, alleging the Russians had the “strategic goal to sow discord in the U.S. political system.”

The DNC lawsuit alleges the Trump campaign acted like a “racketeering enterprise,” saying Trump associates and employees of WikiLeaks encouraged Russia to hack into the DNC, “with the expectation that WikiLeaks and Assange would disseminate those secrets and increase the Trump Campaign’s chance of winning the election.”

Lawyers for the DNC laid out their claims in detail, starting with Mr. Trump’s trips to Moscow in the 1980s to negotiate potential real-estate deals. They point to “laudatory” statements that Mr. Trump made about Russian President Vladimir Putin on the campaign trail, which the DNC says indicated Mr. Trump would adopt policies that favored Russia.

In March, the Trump administration slapped Russia with its first sanctions for election meddling, a year after Congress passed a law forcing White House action. The Trump administration has come under heavy criticism for its response to Russia’s alleged election interference, with critics saying the administration hasn’t taken on Moscow aggressively.

The DNC lawsuit alleges Russian operatives launched cyberattacks on the DNC in 2015 and 2016 to take large volumes of documents, and that WikiLeaks made its first major release of stolen DNC emails and documents after a June 2016 meeting in New York’s Trump Tower between Trump campaign operatives and a Russian lawyer.

Foreign governments can be shielded from civil lawsuits by a legal doctrine known as “sovereign immunity,” but the DNC said Russia isn’t entitled to that immunity because the lawsuit’s claims arise out of Moscow’s “trespass onto the DNC’s private servers...to steal trade secrets and commit economic espionage,” which directly affects the U.S.

Write to Nicole Hong at nicole.hong@wsj.com and Julie Bykowicz at julie.bykowicz@wsj.com