Two rezoning bills integral to Mayor Bill de Blasio’s plan to increase the city’s stock of lower-rent apartments passed Thursday in committee votes and are poised for approval next week by the full City Council.

“We need this housing badly,” said Council member Donovan Richards (D-Queens), chair of the zoning subcommittee.

He pointed to changes made after talks between the lawmakers and de Blasio’s aides that add incentives for developers to build more units for lower-income New Yorkers and adjust design standards to preserve the character of different neighborhoods.

The council, for example, won a builder option that sets aside 20 percent of units for families earning less than $31,000. De Blasio’s original options were for the $46,000-to-$93,000 range.

The legislation, “as modified, will be a huge improvement over existing city policy,” Donovan said.

The latest tier of approvals comes after months of contentious meetings, hearings and protests by community and borough boards and housing and labor activists over a variety of issues.

De Blasio has won allies steadily and the council is celebrating the compromises it secured.

“We want you to know that we heard you loud and clear,” said Council member David Greenfield (D-Brooklyn), chair of the land use committee that also passed the modified measures.

Council member Jumaane Williams (D-Brooklyn) voted against the mandatory inclusionary housing bill because he said it doesn’t do enough for the poor. A neighborhood could shut out low-income families by choosing the higher-rent options, he said.

“We have to break up the segregated communities that are in this city,” Williams said.

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