Northern Virginia leaders are weighing in this week on a controversial state plan to add tolls to Interstate 66 lanes inside the Capital Beltway.

But leaders in Fairfax and Arlington counties are at odds over a key component of the plan: At what point should an extra lane be added to relieve congestion on one of the nation’s busiest highways?

The Fairfax County Board of Supervisors voted Tuesday to recommend that state officials begin designing an extra eastbound lane along the 10-mile stretch as soon as possible if the new tolls don’t significantly improve traffic.

Arlington — set to vote on its own recommendations later this week — wants the state to wait until at least 2023 before any road-widening work occurs and is arguing for more commuter buses and rail transportation to be added first.

The narrow highway “needs additional capacity and it needs it now,” said Fairfax County Supervisor Pat Herrity (R-Springfield), before the board approved a list of concerns to send to Gov. Terry McAuliffe (D) and the Northern Virginia Transportation Commission — an entity that will decide how the toll revenue should be spent in the region.

The plan to add tolls to I-66 inside the Beltway, which McAuliffe has championed, has tapped into long-standing frustrations over traffic in the Washington region and became a volatile issue during Virginia elections this month.

State officials expect to formally adopt the plan by year’s end, although Republicans — accusing Democrats of supporting a de facto tax on commuters — are still seeking to defeat it. On Monday, state Del. James M. LeMunyon (R-Fairfax) submitted legislation to be considered during the 2016 General Assembly session that would ban tolls on I-66.

“We just really want to hit the reset button on this whole discussion,” LeMunyon said.

Leaders in Fairfax, Arlington and Falls Church say they want assurances from the state that neighborhoods along the I-66 corridor will not be overwhelmed by extra traffic from motorists seeking to avoid the tolls.

They say the tolls should be low enough that single drivers are willing to pay the price instead of veering onto side roads that are already slammed with traffic. (Under the state plan, commuters who carpool would still be allowed to travel I-66 for free.)

“When you come off the I-66 exit, you’re going to run into a red light within a block,” said Falls Church City Council member David Snyder, who is worried about gridlock.

State officials plan to base the toll amount on the level of traffic congestion on the roadway. The tolls would average $5 or $6 but would be higher during times of heavy traffic — potentially as high as $17 for drivers who traverse the entire length of the highway during the most expensive hours.

On Tuesday, Fairfax officials voted to ask for “reasonable” toll amounts, although they did not say how much drivers should be expected to pay.

“The tolls needs to be reasonable,” said the board’s chairman, Sharon Bulova (D). “Otherwise, people will continue to use the side roads during peak hours and will be drifting onto the other surrounding highways, and that’s not a good outcome.”

Under the state’s proposal, the toll revenue — an estimated $8 million a year — would first go toward improving nearby ancillary roads, adding commuter buses, synchronizing traffic lights and creating bike lanes in an effort to reduce overall congestion along the I-66 corridor.

When it becomes clear that those options are no longer working, the plan calls for expanding I-66 inside the Beltway. The timing of such a project is a source of deep division in the region.

On Tuesday, Fairfax recommended a faster timetable for another eastbound lane — but only after a long debate that ended with a 6-to-4 vote.

Arlington officials argue that expanding the roadway should be considered only after all other options for traffic relief are exhausted. “We are looking to get far more people through this area, without widening,” said Arlington Board member Jay Fisette (D). “That’s the first goal.”

The differences between the two counties boiled over into frustration Tuesday.

“I am, quite frankly, sick and tired of watching an entire region of the state and the state itself have to kowtow to Arlington,” said Fairfax County Supervisor John Cook (R-Braddock).

Virginia Transportation Secretary Aubrey L. Layne Jr. said it is inevitable that an extra lane on I-66 will be needed, although probably not for a few years. “Nobody is under the impression that some kind of expansion is not going to be needed,” Layne said. “It’s going to be.”

He said the state is hoping that the tolls act as a deterrent to solo drivers, who are violating state law by traveling along I-66 inside the Beltway during peak rush hours.

“The key thing to remember today is, if you’re a sole occupant, you can’t use the road,” Layne said. “If we do nothing, everybody loses.”