The meeting is the second time LaHood has waded into the Virginia project. Last year, he negotiated a resolution between local leaders to keep the proposal to build the second half of the line on track.
The first phase of construction of the railway, which is scheduled to open next year, is being built with the help of a $900 million grant from the Federal Transit Administration.
But the second phase of the project is once again at a impasse. Republican leaders in the state legislature have expressed dismay at a provision in construction plans to give preference in contracting to companies that use unionized workers.
The plans were drafted by the airport board that was appointed mostly by Democrats. Virginia GOP leaders have threatened to withhold funding, citing cost overruns on the first phase of the railway.
A Virginia congressman, Rep. Frank Wolf (R), introduced a bill to create an inspector general to oversee the MWAA, and some GOP leaders in Virginia have suggested transferring responsibility for the project to the state.
But LaHood said in the interview Wednesday that he was confident he could be a peacemaker again.
"This is a project that will go forward," he said. "This is a project that is absolutely essential to delivering people around this region.
"I have every confidence we will be able to find a path forward to make the Silver Line a complete line all the way to Dulles airport and beyond into Loudoun County," LaHood continued.