The police border control division at Arlanda Airport opened an investigation as a matter of course after receiving the complaint Tuesday, spokeswoman Jessica Fremnell said.
She declined to comment on Assange's suggestion to interrogate people in Obama's entourage, saying "we make our own decisions about what we think we need to do."
Assange's lawyer, Per Samuelson, told the AP that airport personnel in Berlin and Stockholm had not been able to locate the bag and could not explain how it got lost as Assange traveled to Berlin on Sept. 27, 2010.
"It was checked in and we have luggage tags and everything," he said. "It's gone without a trace."
WikiLeaks spokesman Kristinn Hrafnsson said similar complaints would be filed in other countries, including Germany and Denmark, alleging potentially unlawful U.S. intelligence operations against Assange.
"It's time to confront it and fight back on all fronts," Hrafnsson told the AP.
WikiLeaks has published tens of thousands of pages of secret U.S. diplomatic and military communications over the last few years, deeply angering the Obama administration. U.S. Army Pvt. Chelsea Manning, previously known as Bradley Manning, was recently sentenced to 35 years in prison for giving U.S. government secrets to WikiLeaks.
According to Assange's affidavit, the missing suitcase contained evidence of a "massacre" of civilians by U.S. military forces in Garani, Afghanistan.
A U.S. Army investigation concluded that a 2009 airstrike killed 26 civilians, at least 78 Taliban fighters and five Afghan police in the village of Garani. Local officials said the attack killed 140 villagers. It was not immediately clear if this was the event Assange was referring to.
At Manning's court-martial, prosecutors tried unsuccessfully to connect Manning to an encrypted Garani video placed in December 2009 on the computer of a Brookhaven National Laboratory worker.
Assange's affidavit also accuses U.S. military intelligence of monitoring his "journalistic activities" while he attended a conference in Berlin in December 2009 and using that surveillance to assist in the prosecution of Manning.
A German newspaper reported that Assange filed a criminal complaint Tuesday against a former U.S. Marine for allegedly spying on him in Berlin in 2009.
The Sueddeutsche Zeitung said the charges were filed at the Federal Prosecutor's office in Karlsruhe. The office did not immediately respond to an AP request for comment.
According to the paper, the unnamed U.S. soldier, who was based in Germany from 2006-2010, also worked in intelligence and spied on Assange while he attended a 2009 Chaos Computer Club meeting in Berlin. It reported the Marine was also a witness in the trial against Manning.
Assange has been holed up for more than a year at Ecuador's Embassy in London to avoid being extradited to Sweden on sex crimes allegations.
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Associated Press writers Kirsten Grieshaber in Berlin and Dave Dishneau in Hagerstown, Maryland, contributed to this report.
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Karl Ritter can be reached on https://twitter.com/Karl_Ritter