Nominees for secretary of state are not required by committee rules to provide tax returns.
A standard questionnaire sent jointly by Democrats and Republicans asks whether the nominee would be willing to provide prior tax returns for himself and his spouse "if asked." Three Senate Democrats told CNN Tillerson answered this question in the affirmative.
But Tillerson pledged only to provide "information" about the tax returns, not the return itself, according to two sources familiar with his questionnaire.
When asked for clarification by CNN, a committee aide said Tillerson wrote in the questionnaire: "If asked, I will make tax return information from the past three years available on a confidential basis for appropriate review."
A Democratic request for Tillerson's tax returns was submitted in writing to the transition, according to a senior Democratic aide familiar with the communications.
"It is frustrating because last week it appeared that there was clear communication between the transition team and both majority and minority staff about this issue," the aide said. "Obviously, something changed."
But Bob Corker, the Republican chairman of the Senate Foreign Relations Committee, says nominees are never asked to provide the documents.
"As is long-standing precedent for nominees considered by the Senate Foreign Relations Committee, the committee has not asked Mr. Tillerson to provide his tax returns," Corker told CNN in a statement. "He will submit an extensive financial disclosure, which is expected to be received in coming days. Our committee plans to carry out exactly the same procedures for Mr. Tillerson's nomination that have been carried out since well before I joined the committee 10 years ago."
Trump's transition team declined several requests for comment.
Democrats argue that Tillerson, the chief executive of ExxonMobil who has come under fire for his ties to Russian President Vladimir Putin, is a special case warranting further scrutiny. They also acknowledge they're pushing for the tax returns of Tillerson and other Cabinet nominees to highlight Trump's continued refusal so far to release his own records.
Corker, who was a finalist for the secretary of state job himself, tweeted last week he had a "very good conversation with Secretary of State nominee Rex Tillerson yesterday and am looking forward to meeting with him in January."
He added: "Also appreciated a call I received from President George W. Bush, who spoke highly of Mr. Tillerson and offered support for his nomination."
Tillerson completed the Foreign Relations Committee's lengthy questionnaire on Friday evening
, but has yet to submit personal financial disclosure documents, a committee aide told CNN on Tuesday. The documents likely contain new, previously unpublicized information about Tillerson, who has maintained a relatively low profile throughout his private sector career. The files have not been publicly disclosed and remain in the hands of committee staff.
Tillerson will have to first be confirmed by Corker's panel and then the full Senate to become the nation's top diplomat. But he has met resistance from some Senate Republicans because of his relationship with Putin.
If Democrats unite against his nomination, he can't afford to lose the support of many GOP senators.
Tillerson has quietly started to make the rounds on Capitol Hill, allaying concerns from some Russia hardliners such as Sen. Tom Cotton of Arkansas and Sen. Ron Johnson of Wisconsin, a key vote on the Foreign Relations Committee.
Johnson told CNN Tuesday that Tillerson told him he'd play a "different role" as a businessman than he would as secretary of state, downplaying the relationship with Putin.
Senate Majority Leader Mitch McConnell said Monday night that he disagreed with Tillerson's past opposition over imposing sanctions on Russia, but said that Tillerson was "representing his company" at the time.
"My guess is that Vladimir Putin will be very disappointed with" Tillerson as secretary of state, McConnell told KET in Kentucky.
CNN's Jeremy Diamond contributed to this report.