The motion, proposed by member of the London Assembly Hina Bokhari, also requested for the establishment of a fire safety victims support hub and the trial of a public fire safety risk assessment register in the capital.
The register will be similar to the Energy Performance Certificates and enable prospective buyers or renters to see the fire safety rating of a home.
Additionally, the mayor was asked to ensure both Building Safety Fund and Waking Watch Relief Fund applicants hear back from the Greater London Authority regarding their applications in a timely manner.
The Assembly is also lobbying the central government to remove the burden of remediation costs from leaseholders.
Bokhari said: “We need to listen victims of this crisis and represent their needs.
“Of course the government needs to do more to comprehensively deal with the building safety crisis, and many of us will keep pushing for this. Yet it is too easy just to call on the government. We need to look at the levers and powers the mayor has to ensure far more is done to support those affected by this shameful scandal in London.
She added: “With an affordable housing budget of over £4bn the mayor could send a clear message to developers by refusing to work with those who are yet to take action to remediate fire safety issues in their existing stock. There are numerous other actions the mayor could take to support leaseholders.
“We need the mayor to couple warm words with action. As well as lobbying government he needs to use his powers and levers to their full extent to give practical support to the thousands of Londoners impacted by this terrible scandal.”