The San Francisco Board of Supervisors gave unanimous initial approval Tuesday for an ordinance that will allow residents temporarily displaced by fires or natural disasters to rent other apartments at below-market rates.

The proposal, introduced by Supervisor Scott Wiener in February, would allow tenants to enter an agreement for up to two years at either what they were paying at their previous residences or up to 10 percent above that rate.

Wiener said Tuesday that this is a “long overdue measure” that will help tenants displaced by fires, earthquakes or other disasters.

He said a major earthquake is bound to hit San Francisco in the coming years “and we got a reminder again [Monday] when there was a minor one,” a 3.4-magnitude quake that shook parts of The City.

Wiener said landlords are willing to rent apartments to tenants on a temporary basis, but under the current housing laws, they cannot offer them at below-market rates temporarily without locking in that rate as the rent-control base rent.

He said the ordinance initially approved Tuesday has the support of both the San Francisco Tenants Union and the San Francisco Apartment Association.

The ordinance will come in front of the board again next week for final approval.