Jensen told broadcaster DR that he was now considering placing the development in an alternative location.
“We are no longer planning to build at the site we had planned. We are now planning to build somewhere else,” Jensen said.
A viability study is being carried out as to whether the development can be moved to “another place” just a few hundred metres to the west of the original site at Amager Fælled, according to the broadcaster's report.
Plans already exist for a camping site at the second location, but the area is protected, meaning that parliament would have to approve any development at the location, writes DR.
Jensen said he expected results of the feasibility study to be available at the beginning of 2018.
The Social Democrat mayor was previously a strong supporter of developing the original site at the Strandengen area of Amager Fælled.
But after council members from the Venstre (Liberal) party voted in support of moving the project, Jensen was forced to change his own position.
“I have listened and can see that I no longer have majority support amongst the parties that were originally part of the decision on what should be built in the Ørestad region to finance the building of the Metro, a decision we took 25 years ago,” he told DR.
19 hectares, around six percent of the natural environment at Amager Fælled, would be turned into around 2,500 homes by the project. The decision to sell the land for building homes was made in 1994 as part of a plan to raise funds to build the Metro, writes the broadcaster.
The project would bring in two billion kroner to Copenhagen Municipality – which is in need of the funds to pay off costs of the now-built underground train system, Jensen said.
“I do not want to send this bill to our children and grandchildren,” he said.
The decision to build on the Amager Fælled natural area has met with strong criticism.
Over 47,000 people have signed a petition with the Danish Society for Nature Conservation (Danmarks Naturfredningsforening) against the project, arguing that the Strandengen area is the last original natural environment left in the Copenhagen municipal area.
In May this year, several thousand people took part in a demonstration at the location.
“I have, of course, also listened to the massive criticism Copenhageners around town have for building at this particular place,” Jensen told DR.