"I think Russian authorities have information that would be incredibly helpful that they haven't provided yet," Rogers said.
On Fox News Sunday, House Homeland Security Committee Chairman Michael McCaul (R., Texas) said he had discussed the involvement of "trainers" with the FBI.
"I think, given the level of sophistication of this device, the fact that the pressure cooker is a signature device that goes back to Pakistan, Afghanistan, leads me to believe . . . that there was a trainer," McCaul said. "And the question is, where is that trainer or trainers?
"Are they overseas in the Chechen region or are they in the United States?" he asked. "In my conversations with the FBI, that's the big question. They've cast a wide net both overseas and in the United States to find out where this person is. But I think the experts all agree that there is someone who did train these two individuals."
Rep. Adam Schiff (D., Calif.), who sits on the House Intelligence Committee, told CNN's State of the Union that he also believes the Russians "know more than they're telling us." He said he wanted to know why Russian authorities recorded a conversation between Tamerlan Tsarnaev and his mother. "We don't know that," Schiff said. "We haven't received that information from the Russians."
It is not clear how exactly the brothers became radicalized, he said, though he said there probably was no link to a major terrorist group. "It does look like a lot of radicalization was self-radicalization online, but we don't know the full answers yet," he said.
On the Sunday news programs, several lawmakers critiqued the way authorities handled the Boston bombing, from the failure to identify the Tsarnaev brothers as threats to the decision to read the surviving suspect a Miranda warning after 16 hours of questioning.
"I was very surprised that they moved as quickly as they did" on reading Dzhokhar Tsarnaev his Miranda warning, Sen. Daniel Coats (R., Ind.) said on CNN. "We have legal reasons and follow-up investigative reasons to drag this out a little bit longer.
"We could have done that."
On Fox News Sunday, Sen. Joe Manchin (D., W.Va.) also argued that authorities "pulled the trigger too soon" in delivering the Miranda warning to the surviving alleged bomber.
Rep. Peter King (R., N.Y.) said on Meet the Press that the FBI "did an outstanding job in solving this" after the attack. But he added that "I don't think they did a full investigation" when first asked to look into Tamerlan Tsarnaev, the older brother who died in a firefight with police.
"They never went to his mosque, never spoke to his imam, never spoke to a number of his relatives," and never flagged Tsarnaev to the Boston police, King said.
McCaul criticized authorities for telling news organizations that no connection had yet been made to a foreign terrorist organization or individual.
"What I found astounding is that right out of the box, U.S. officials anonymously are saying there's no foreign connection to this case," McCaul said on Fox News Sunday.
"The FBI just began their investigation in this case."