This is the first time that Transport for London has acknowledged that the levy is having an effect on contractors.
Gavron, speaking at the MIPIM property festival in Cannes on the French Riviera last week, said she would report back to Transport for London on the concerns raised by readers of Building over the charge. Gavron said she would highlight the impact on smaller firms.
She added that Transport for London could act in an advisory capacity for contractors on the issue. She said: "It is up to us to be able to advise contractors. We could hold a construction round table meeting to discuss the issue."
Gavron indicated that contractors has no chance of winning an exemption unless they reviewed their transport policies. She said: "It is time for contractors to clean up their act and start innovating and producing new ideas to help counter costs of the charge."
She cited lorry pooling and modifying vehicles to operate on greener fuels as examples of innovation that might be looked on favourably.
Building launched the Chop the Charge campaign last month with the aim of gaining an exemption for construction firms.
It noted that industry associations had failed to lobby London mayor Ken Livingstone over the issue.
Dozens of Building readers have since pledged support for the Chop the Charge campaign, claiming that the charge has had a severe impact on business and is a tax on development.
Transport for London refused to consider an exemption when approached for the first time by Building three weeks ago. Gavron's announcement that she will meet industry leaders marks a shift in opinion, and gives industry leaders a chance to put their case in person.
n David Fison, chief executive of Skanska, is the latest high-profile figure to throw their weight behind the campaign.
Fison said: "People and vehicles specifically engaged in repairing or building the infrastructure needed to sustain London must be exempt."