A spokesman for Barkat said on Monday that the municipality had finished those consultations.
"Now, after fine-tuning the plan and seeking more co-operation with the residents... the municipality is ready to submit the plans for the first stage of approval," Stephan Miller, Barkat's spokesman, said.
The plan still must undergo several additional approvals before any demolitions take place. The Jerusalem planning committee is the municipal body responsible for approving all construction in the city.
Activists in Silwan denounced the latest move as another step in the "fast-track Judaisation" of East Jerusalem.
Al Jazeera's Jacky Rowland last year interviewed Silwan families with homes slated for demolition
It pre-empts "the possibility of Jerusalem ever being a shared city, or indeed capital of a Palestinian state," they said in a statement. "This in itself precludes peace."
Several members of Meretz, a left-wing Israeli political party, threatened to resign their seats on Jerusalem's city council over the announcement.
Mark Regev, Netanyahu's spokesman, said the prime minister still wants more dialogue with the affected families.
"This is a preliminary planning procedure and it still gives time, more than enough time, for dialogue to continue," he said.
PJ Crowley, a spokesman for the US state department, said the US government was "concerned" about the announcement.
"This is expressly the kind of step that we think undermines trust that is fundamental to making progress to the proximity talks and ultimately to direct negotiations," Crowley said.
The Palestinian Authority has not yet commented on Monday's decision. Muhammad Ishtayeh, a PA cabinet minister, said after the plan was announced in March that there was "no way" Palestinians could accept it.
The 'King’s Garden'
The Palestinian homes targeted for demolition are in Silwan’s al-Bustan quarter, which Israel calls Gan Hamelech - the "King's Garden" - because the biblical King David supposedly wrote his psalms in the neighbourhood.
The homes would be razed and replaced with a collection of shops, restaurants, art galleries and a large community centre.
Israeli officials say the displaced families would be allowed to build new homes elsewhere in the neighbourhood - but haven’t said whether they will compensate those families for their losses.
Israeli officials say that all of the 88 Palestinian homes in Silwan are built illegally. It is extremely difficult for Palestinians to obtain construction permits in East Jerusalem, so many families build their homes without the required paperwork.
Barkat's proposal would allow residents of the other 66 Silwan homes - the ones not slated for demolition - to retroactively apply for construction permits, according to a report in the Jerusalem Post.