WASHINGTON — For more than a decade, questions have lingered about the possible role of the Saudi government in the attacks on Sept. 11, 2001, even as the royal kingdom has made itself a crucial counterterrorism partner in the eyes of American diplomats.

Now, in sworn statements that seem likely to reignite the debate, two former senators who were privy to top secret information on the Saudis’ activities say they believe that the Saudi government might have played a direct role in the terrorist attacks.

“I am convinced that there was a direct line between at least some of the terrorists who carried out the September 11th attacks and the government of Saudi Arabia,” former Senator Bob Graham, Democrat of Florida, said in an affidavit filed as part of a lawsuit brought against the Saudi government and dozens of institutions in the country by families of Sept. 11 victims and others. Mr. Graham led a joint 2002 Congressional inquiry into the attacks.

His former Senate colleague, Bob Kerrey of Nebraska, a Democrat who served on the separate 9/11 Commission, said in a sworn affidavit of his own in the case that “significant questions remain unanswered” about the role of Saudi institutions. “Evidence relating to the plausible involvement of possible Saudi government agents in the September 11th attacks has never been fully pursued,” Mr. Kerrey said.