THE MBTA’S FISCAL MANAGEMENT AND CONTROL BOARD on Monday approved spending another $15 million on the Green Line extension even as state officials said they expected to hear this week whether the federal government would honor its earlier commitment to provide $1 billion for the project.

John Englander, the MBTA’s legal counsel, said the T has spent $4.5 million of a $6 million authorization and needs up to $15 million more to move ahead with developing specifications for a future construction contract. The work at the T is proceeding even as the authority is trying to convince Federal Transit Agency officials to support a streamlined redesign of the project and commit to providing the $1 billion they initially pledged.

The extension of the Green Line into Somerville and Medford was put on hold when cost estimates for the project ballooned from $2 billion to $3 billion. T officials, with the help of outside contractors, redesigned the project to reduce costs and solicited additional financial support from Somerville and Cambridge.

Jack Wright, the private contractor leading the interim redesign effort, said federal officials are coming into town this week for meetings where they are expected to say how they view the T’s redesign. He said the T should have a much better handle on whether the federal government will provide the $1 billion after those meetings.

“I don’t think it’s like a blessing,” Wright said of the federal review. Still, he said, it’s important. “It’s one of the big key steps.”