A scaled-down design for the trolley extension to Somerville and Medford, aimed at reining in the project's bloated budget, appears consistent with the aims of the overall effort, according to a top official at the federal agency that pledged $1 billion to the earlier version.

In a Friday letter, Mary Beth Mello, regional administrator for the Federal Transit Administration, noted additional analysis is needed on the revised plans' accessibility, risks, and the state's ability to finance the endeavor.

Before amending the grant agreement, the federal agency "must have every confidence the MBTA can deliver the entire scope of the redesigned GLX within the specified budget and schedule," Mello wrote.

Even after Somerville and Cambridge recently agreed to contribute a combined $75 million and a planning organization shifted $152 million of federal highway dollars into the seven-station expansion, MBTA officials face an estimated $73 million funding gap.

Expected to serve 50,000 riders, the extension would rebuild the northern terminus of the line in East Cambridge and build another six trolley stations. Transit advocates are hoping for one more station further out in Medford.

Pegged at $2 billion in the final stretch of the Patrick administration, the project was halted last summer by the Baker administration after its cost estimate grew to as much as $3 billion.

Over the past several months, consultants and T officials have scaled down the scope of the project, removing fare gates and a superstructure that would have carried a community path.

Mello praised the efforts of the interim project management team, led by Jack Wright, commending the group "for its diligence and extraordinary efforts to revive the Green Line Extension in the face of your fiscal challenges."

During the redesign, Transportation Secretary Stephanie Pollack and others cautioned that a substantial change to the project could imperil the $1 billion federal grant.

Friday's letter, which the Boston Globe reported on Friday afternoon, appears to put those concerns to rest for now.

"It is the preliminary view of both headquarter and regional staff of the Federal Transit Administration (FTA) that the proposed re-scoping of the GLX is consistent with the scope of work and the expected benefits of the original project that was the subject of the Full Funding Grant Agreement," Mello wrote to Pollack.

Mello said the timing of the FTA review "will depend on the level of design and detail you make available, the onboarding of your new project management team, and any questions that may arise in our reviews."

Earlier this month the MBTA's Fiscal and Management Control Board and the Massachusetts Department of Transportation Board of Directors agreed to advance the project. The missing $75 million - a number that officials said might grow upon review - could lead to future debates over funding sources.

"MassDOT and the MBTA appreciate the FTA's initial feedback and the departments look forward to continuing to work with our federal partners on the new design," Pollack said in a statement.