JUNEAU — The state budget remained unsettled Thursday, one-third of the way through the special session called by Gov. Bill Walker.

Lawmakers are scheduled to reconvene Tuesday; the Legislature last week voted for a recess in floor sessions until then.

But House Speaker Mike Chenault, R-Nikiski, and Senate Majority Leader John Coghill, R-North Pole, questioned bringing the full Legislature back to Juneau to gavel in if there is nothing new to act upon. Both hoped to have greater clarity in the next few days.

A spokeswoman for Walker said the governor expects lawmakers back in Juneau on Tuesday.

This week, the House Finance Committee has held budget hearings in the Anchorage legislative office building; Senate Finance held a meeting at the Capitol on Monday. Behind-the-scenes budget talks have continued, legislative leaders said.

On Thursday afternoon, the drone of equipment could be heard throughout the Capitol as part of scheduled renovation work on the building.

Jesse Kiehl, an aide to Juneau Sen. Dennis Egan and a local Assembly member, said meeting space would be available for the Legislature at Centennial Hall and a local arts center. Kiehl said many offices in the Capitol could still be used and efforts were underway to secure alternate office space for lawmakers. Members of the Juneau delegation have offered help in finding hotel space or other lodging for legislators and staff.

Walker called a special session last week, after legislators failed to reach agreement on a fully funded budget for the fiscal year beginning July 1. The House fell short of the votes needed to tap the constitutional budget reserve fund to cover costs. Support from the Democratic-led minority was needed to reach the required threshold, but minority members opposed the budget’s cuts to education and its rejection of negotiated pay raises for union contracts, among other things. Minority members also want expanded Medicaid.

The House and Senate GOP-led majorities have resisted adding money to the budget and balked at minority-offered alternatives to offset costs, like revisiting the state’s oil tax credit system.

Senate Finance Committee co-chairman Pete Kelly said in a phone interview that he thinks the budget can be sorted out before the end of this special session. He wasn’t so sure on Medicaid expansion, another issue on Walker’s special session call.

The first order of business has to be getting the governor a budget he can work with, said Kelly, R-Fairbanks, adding that Medicaid is a major policy discussion that he believes can be taken up at a later time.