Boston received about 5,500 verified applications by the deadline last Friday from residents seeking help paying their rent, according to city housing officials.

About 800 applicants are to be chosen by lottery to have full or partial payments of one month’s rent sent to their landlords, a housing official said. The money for the rental relief program, which is being managed by the Office of Housing Stability, will come out of a $3 million fund created earlier this month by reallocating money from city programs paused due to the pandemic.

During the five-day application period, the city received more than 7,500 requests for rental assistance. Only 5,500 were determined to be Boston residents.

“We moved very quickly. We wanted to get funding on the street,” said Sheila Dillon, the city’s housing chief, said of the narrow application window. “Now that we’re starting to understand the resources that we’re going to be receiving from the federal government, we do anticipate having multiple additional rounds.”

Dillon said the forthcoming federal funding will be placed in the fund in the coming weeks.

The announcement comes after some criticism over the short duration of the application period and the ways residents were notified that the financial assistance was available.

In a statement to WGBH News Monday, City Councilor Michelle Wu said the city needed to prioritize equity in its response to the coronavirus outbreak.

“Conducting a lottery for the first batch of people connected enough to apply may be a way to dole out limited funds quickly, but not equitably,” she said. “With a tight deadline, when multilingual materials weren’t distributed until later in the process, and when residents had to proactively apply, many who most need relief will be left out.”

Each household selected in the lottery will be eligible for up to $4,000 in rental assistance. Preference, Dillon said, will go to households that are not receiving unemployment benefits and those that are not receiving enough unemployment benefits to cover their expenses.

“We know there are a lot of jobs out there that either can’t access unemployment benefits … or, the unemployment benefits that they can access are much less than what their income was,” Dillon said, pointing to both undocumented and tipped workers. “We knew that those groups would be hardest hit, and those are who we are prioritizing for the fund.”

Applicants selected through the lottery will have to go through a supplemental application demonstrating their need and inability to pay. The goal is to begin disbursing funds before the end of the month.

Dillon added that the office is still encouraging people to find additional help from other sources.

“It’s going to be impossible for the city to meet everyone’s needs, so we really do want people to access every resource that they can,” she said.