In areas covered by Ulez, drivers are charged £12.50 per day for cars that do not meet emissions standards.
It is due to be extended beyond central-London to all 32 boroughs on August 29.
Khan has argued strongly the programme is necessary to protect public health, with air pollution causing 4,000 premature deaths in the city.
But Labour’s narrow failure to snatch Boris Johnson’s old seat of Uxbridge from the Tories last month was blamed on the looming imposition of the charge.
The Conservatives tried to turn the by-election into a referendum on Ulez and the victorious Tory candidate credited its supposed unpopularity for his win.
It also triggered a public split between Khan and Keir Starmer, with the Labour leader urging the mayor to “reflect” on the policy.
Danny Beales, Labour’s candidate in Uxbridge, was more forthright, attacking it as “bad policy” that “cut us off at the knees” in his campaign.
On Friday Khan announced a change to the programme that Labour will hope can bridge the divide.
From August 21, all Londoners will be able to apply for a £2,000 grant to replace their vehicle if it is not compliant with the air quality law.
Previously the scrappage scheme was only available to people on certain benefits, businesses with fewer than 50 employees and charities based in London.
“I have always said that expanding the Ulez to the whole of London was a difficult decision, and not one I took lightly – but it’s a decision I remain committed to seeing through,” Khan said.
“I’m not prepared to step back, delay or water down vital green policies like Ulez, which will not only save lives and protect children’s lungs by cleaning up our polluted air, but help us to fight the climate crisis.”
It was given a cautious welcome by Beales as a “step forward”, who added: “I hope the mayor keeps listening and assessing the impact on businesses and low paid workers.”
The row over Ulez has also moved beyond that one policy, with Rishi Sunak coming under pressure from Tory MPs to ditch the party’s commitment to several environmental policies.
And the prime minister has already ordered the Department for Transport (DfT) to carry out a review of low traffic neighbourhoods (LTNs).