Complaining that the Post was losing dollars 300,000 (pounds 198,500) a week despite years of cost-cutting, News Corporation said the tabloid had to be economically viable.
It is insisting on new concessions from its 700 unionised employees, including the right to fire anyone during the next six months without paying their redundancy costs.
News Corporation won the right to publish the Post, which is currently in bankruptcy, in April and last week received approval from the US Federal Communications Commission to buy the paper.
But late on Tuesday, the Post's interim publisher, News America's chief executive Patrick Purcell, gave the bankruptcy court the required three-day notice of closure.
'One absolute condition of our acquisition of the paper was reaching satisfactory labour agreements,' he told the court.
If Mr Murdoch carried out his threat, control of the newspaper would revert to the creditors of its bankrupt owner, the property developer Peter Kalikow. But it seems unlikely that another potential saviour would emerge to publish the paper.
News Corporation has been negotiating with the Post's 11 trade unions since late March and claims to have reached 'understandings' with some leaders, although others are said to have suspended talks.
Members of the largest union, the 300-member Newspaper Guild, who were due to hold an emergency meeting last night, have authorised their leaders to call a strike.
Leaders of the Guild, which represents the tabloid's editorial and advertising staff, said it was 'absolutely out of the question' that they would accept News Corporation's demands for a six-month 'evaluation period'.
The company wants to be allowed to fire employees, some with more than a decade's service, without severance pay.
Other sticking points include the contracting out of work and the removal of advertising personnel from the union agreement.
But analysts said Mr Murdoch was already in a strong position to remake the tabloid, with so many of the Post's staff having left for jobs elsewhere.
Large numbers of the paper's present editors and managers are in fact on loan from his other American tabloid, the Boston Herald. Journalists from other News Corporation publications have also being approached about working at the Post.Reuse content