Boston Bombing Suspect Under FBI Surveillance For At Least 3 Years, Mother Says

* Mother says she believes sons were framed

* Tells Russian interviewer FBI was monitoring older son

* Both parents says Internet use was monitored (Adds father, details from mother)

By Timothy Heritage

MOSCOW, April 20 (Reuters) - One of the two ethnic Chechens suspected by U.S. officials of being behind the Boston Marathon bombings had been under FBI surveillance for at least three years, his mother said.

Zubeidat Tsarnaeva told the English-language Russia Today state television station in a phone interview, a recording of which was obtained by Reuters, that she believed her sons were innocent and had been framed.

Tamerlan Tsarnaev, 26, was killed in a shootout with police and his 19-year-old brother Dzhokhar was captured after a day-long manhunt.

"He (Tamerlan) was 'controlled' by the FBI, like, for three to five years," she said, speaking in English and using the direct English translation of a word in Russian that means monitored.

"They knew what my son was doing, they knew what sites on the Internet he was going to," she said in what Russia Today described as a call from Makhachkala, where she lives in Russia's Dagestan region after returning from the United States.

Tsarnaeva echoed the boys' father, Anzor, who said on Friday that he believed they had been framed. Both suggested in separate interviews that the FBI had made no secret of the fact that at least one of the brothers was being watched.

"I do not believe that my sons could have planned and organised the terrorist act, because they knew U.S. national security services were keeping an eye on them," Anzor Tsarnaev told Russia's Channel One television.

"They (the security services) said 'We know what you eat, what you read on the Internet'," he said, without making clear how the security officers had made contact.

In her interview with Russia Today, Tsarnaeva suggested FBI officers had visited her home when she still lived in the United States and told her that Tamerlan "was really an extremist leader and that they were afraid of him."

"It is really, really a hard thing to hear. And being a mother, what I can say is that I am really sure, I am, like, 100 percent sure, that this is a set-up," she said.

She did not say whether the FBI had started to take an interest in Tamerlan although she also referred to the security services' interest in what Internet sites he visited.

U.S. government officials have said the brothers were not under surveillance as possible militants.

But the FBI said in a statement on Friday that in 2011 it interviewed Tamerlan at the request of a foreign government, which it did not identify.

It said the matter was closed because interviews with Tamerlan and family members "did not find any terrorism activity, domestic or foreign".

The FBI statement was the first evidence that the family had come to security officials' attention after they emigrated to the United States from Dagestan about a decade ago.