More than 1,000 new demolition orders have been issued in Nir Barkat’s first six months in office, the Association for Civil Rights in Israel said.
Many Palestinian and Arab residents of the city build illegally because of difficulties getting building permits.
The municipality said the Acri report was deceptive and inaccurate.
“There have been no changes to the city’s enforcement policy [of demolition orders], nor has the mayor given any orders to increase the rate,” the municipality said.
Building in mainly Arab East Jerusalem is a highly politicised issue.
The Palestinians want the area to be the capital of a future state, while Jewish groups are trying to increase the number of Jewish settlements there.
While Mr Barkat has said he intends to streamline the application process for building permits, Acri said the municipality had added two new requirements to the process, which would make it harder for Israeli Arabs and Palestinians to get permission to build.
In a recent decision he also allocated only 7% of funds of a recent, interim budget to East Jerusalem, while the rest went to the Israeli west of the city, Acri said.
The Jerusalem municipality said this was misleading, and funds were not allocated geographically.
“In terms of Barkat’s actions and budget allocations, there appears so far to be no connection between promises and deeds, and thus there is difference between him and his predecessors; Barkat also neglects and discriminates,” the report said.
According to figures released by Acri, 67% of families are under the poverty line in East Jerusalem, compared to 23% in West Jerusalem.
It says there is a shortage of 1,500 classrooms in the district, with a 50% drop-out rate and 9,000 children not attending school.
But the municipality said Mr Barkat had made improving the quality of life in East Jerusalem a priority.
“Attempts to blame Barkat, who has been in office for less than six months, for the failures of the government and the municipality for 40 years are populist,” the municipality said.
Earlier this month, the UN asked Israel to freeze all pending demolition orders in East Jerusalem and to do more to provide for the housing needs of Palestinians.
Israel has occupied East Jerusalem since 1967. It has annexed the city and declared its east and west Israel’s eternal capital.
This is not recognised by the international community, with the east of the city considered occupied territory.