Waka Kotahi is looking at whether to reconsider a trial of making space on Auckland Harbour Bridge for walkers and cyclists.
Environmentalist transport lobbyists had threatened it with legal action for deciding against a trial.
The harbour bridge remains a huge obstacle to cross-city alternative transport links after the agency's plans for a hugely expensive second crossing fell through last year.
The government last year asked about running a trial at a "quiet" time of year.
But instead the agency offered to hold a one-day celebratory event on the bridge and began planning for it to run this November.
The lobby group Movement threatened to ask for a judicial review if the agency did not reconsider its opposition to a trial.
The lobby group's lawyers wrote to Waka Kotahi a month ago, saying the minister's request was "a gilt-edged opportunity for WK to break away from the narrow, car-centric thinking that has characterised it for most of its existence and actually do something significant about climate change".
It wants a trial in the bridge's eastern-most lane.
The agency has now replied, saying its 18 August board meeting will look at the request "that Waka Kotahi reconsider its decision on a trial of reallocation of lane space for active modes of transport".
A trial is up to NZTA, not the government.
The agency contended that reallocating a bridge lane would reduce capacity by many thousands of vehicles a day, with nowhere near an equal drop in vehicles on the highway.
Movement said studies did not back this up, or were flawed or misinterpreted, and accused Waka Kotahi of "never seriously" considering having a trial, with its shift to offering to hold an event a "sleight of hand".
Lobbyists and other critics contend the Transport Agency showed its car bias by insisting on paying for cycleway projects out of its walking and cycling budget, even when their costs are forced up by associated upgrades to the state highways alongside.
The Wellington-to-Lower Hutt project was one example, where the budget blew out to over $300 million, for a seawall that will also protect State Highway 2 and the Hutt Valley rail line.
Movement wrote to the agency again today saying it was off track with government goals to shift people out of cars, reduce the road fleet's total mileage and cut emissions.
"We are concerned that NZTA is not giving effect to the minister's expectations," it said in an email to the transport agency's chief executive Nicole Rosie.
"NZTA must stop dedicating the massive state highway and local road improvement activity class budgets for new roading only."
The agency said it would provide an update after the board considers the lobbyist's request later this month.
It had confirmed a supplier for a "series of events" this coming summer that would provide safe bridge access on foot or bike, with dates and route to be confirmed, it said.
It would be free, but with tickets to manage the number of people on the bridge, it said.
"Waka Kotahi will ask motorists to travel at times outside of the events or via other routes so the events are managed safely."