But Snowden indicated in the letter that neither would happen unless the U.S. dropped its espionage charges a policy shift the Obama administration has given no indication it would make.
Stroebele's Thursday meeting with Snowden took place a week after explosive allegations from the Der Spiegel news magazine that the NSA monitored Chancellor Angela Merkel's cellphone prompted her to complain personally to President Barack Obama. The alleged spying has produced the most serious diplomatic tensions between the two allies since Germany opposed the U.S.-led invasion of Iraq in 2003.
Germany's top security official, meanwhile, said he would like to arrange for German authorities to talk to Snowden about those allegations and other U.S. surveillance operations that have enraged Europeans.
Snowden has said he no longer has the NSA materials but his knowledge of U.S. spying efforts could be seen as invaluable by other nations.
"He pointed out that he was active in the U.S. secret services, the NSA and CIA, not just as an administrator or something like that who had access to computers, but also ... participated in operations," Stroebele said of Snowden.
"He noted that he knows a lot about the inner structure ... that means he can, above all, interpret and explain all the documents ...He could explain authentically only as an NSA man could. That means he is a significant witness for Germany too."
In his one-page typed letter, written in English and bearing signatures that Stroebele said were his own and Snowden's, Snowden complained that the U.S. government "continues to treat dissent as defection, and seeks to criminalize political speech with felony charges that provide no defense."
"I am confident that with the support of the international community, the government of the United States will abandon this harmful behavior," Snowden wrote.
But he indicated he wouldn't talk in Germany or elsewhere until "the situation is resolved."
Stroebele said Snowden appeared healthy and cheerful during their meeting at an undisclosed location in Moscow. The German television network ARD, which accompanied Stroebele, said the Germans were taken to the meeting by unidentified "security officials" under "strict secrecy."
"(Snowden) said that he would like most to lay the facts on the table before a committee of the U.S. Congress and explain them," Stroebele said. The lawmaker, a prominent critic of the NSA's alleged activities, said the 30-year-old "did not present himself to me as anti-American or anything like that quite the contrary."
Merkel this week sent German officials to Washington for talks on the spying issue. Germany's parliament is also expected to discuss the NSA's alleged spying on Nov. 18.
Stroebele said he had hoped to meet Snowden in July but contacts with Snowden's side broke off. Stroebele said the contact was re-established at the end of last week about the time the Merkel story broke.
In a video link to an open government conference in London, Kerry said Thursday that because of modern technology, some of the NSA activities have been happening on "automatic pilot" without the knowledge of Obama administration officials.
Kerry said ongoing reviews of U.S. surveillance will ensure that technology is not being abused.
"The president and I have learned of some things that have been happening in many ways on an automatic pilot, because the technology is there," Kerry said. "In some cases, some of these actions have reached too far and we are going to try to make sure it doesn't happen in the future."
Snowden was granted a one-year asylum in Russia in August after being stuck at a Moscow airport for more than a month following his arrival from Hong Kong. Russian President Vladimir Putin has said Snowden got asylum on condition that he wouldn't harm U.S. interests.
Snowden's Russian lawyer, Anatoly Kucherena, told the Interfax news agency that Snowden would not violate the terms of his asylum if he talked to the Germans in Russia about the wiretapping case. But Stroebele said Snowden had "significant reservations" about that idea, fearing that speaking to foreign officials on Russian soil could cause him problems.
If Snowden leaves Russia, he would lose his asylum status, Kucherena confirmed.
Germany, along with many other nations, rejected an asylum request from Snowden earlier this year. In July, the Germans received a U.S. request for Snowden's arrest if he was found in the country.
Snowden's exact whereabouts in Russia and his activities there have been a mystery.
There has been wide speculation that Snowden is under the control of Russia's security services, but there has been no confirmation.
Stroebele was tightlipped about where he met Snowden. The German politician said he had no contact with the German Embassy in Moscow nor with Russian authorities other than a passport control officer although he did not explain who the security officials mentioned by German television were.
Snowden's lawyer says his client has accepted a technical-support job with a major Russian website but refused to name it.
"He enjoys living in Russia ... we have opportunities to visit cultural events. We have opportunities to show him our places of interest," Kucherena said Friday.
He also said Snowden is studying Russian and has developed some competency in it.
The Russian news site Life News on Thursday published a photo showing Snowden apparently on a boat in the Moscow River with the Christ the Savior Cathedral in the background. It said the photo was from September.
"It's him," Kucherena told the AP on Friday.
AP correspondents Vladimir Isachenkov and Jim Heintz in Moscow and David Rising and Robert H. Reid in Berlin contributed to this report.