"It has been alleged that the impasse was somehow connected to gaming," Miller said in the letter the state's 46 other senators. "That is patently untrue."
Miller was not available to comment further on the letter. All three men are Democrats.
The General Assembly failed to pass two budget-related measures to which its leaders had agreed — including a bill to raise income taxes on individuals earning more than $100,000 — when the 90-day session ended at midnight April 9.
As a result, a "doomsday" budget containing roughly $500 million in cuts to state and local programs will take effect July 1 unless the Assembly returns in special session to pass additional legislation.
Busch said Wednesday he didn't know what motivated Miller to send the letter. "I'm assuming this is his version of what he believes took place," Busch said. "I think everyone down here understands what the facts are around the last day of session."
Rick Abbruzzese, a spokesman for O'Malley, declined to comment.
O'Malley has said he will call a special session if the leaders reach agreement on how to avoid the cuts.
It is unclear whether a special session would include action on the gambling bill Miller wants. The Senate president would like to allow a sixth casino in Maryland, to be located in Prince George's County, and allow table games such as blackjack in addition to slot machines at all six casinos.
In the letter, sent Monday, Miller points to the House of Delegates, saying the lower chamber could have done more to prevent the budget cuts. Had the House passed a measure known as the Budget Reconciliation Financing Act, some of the education cuts would have been eliminated, Miller wrote.
Busch reiterated Wednesday that he did not have time to pass that bill — partly because he wanted to spend the final hour of the session working to extend the midnight deadline, an idea that Miller rejected.
The speaker also noted that passing the companion bill without also approving a measure to increase income taxes would solve little. "You would be in the same position you are in today," Busch said.
Miller also cited the Assembly's budget negotiations, saying the Senate gave up considerable ground in the face of an "unprecedented unwillingness to compromise" by the House. The House did not want to increase taxes on those making less than $100,000, and the Senate agreed. Senators had wanted a small tax increase on virtually all incomes.
Miller called the budget impasse a "teachable moment" for citizens to realize that the state can't "cut its way out" of projected budget deficits. He said he is "happy" to return to Annapolis in special session to find a compromise.