Pal Powell, chairman of the Interest-Coordination Forum for Law Enforcement Employees, said that the negotiations would be resumed on Monday, when Prime Minister Viktor Orban will lead government negotiations instead of the Interior Ministry.
The unions are protesting government plans to scrap early retirement.
Over the past few weeks law-enforcement workers and firemen have even taken to the streets to demonstrate against the plan.
Union leaders have held talks with Interior Minister Sandor Pinter. On Thursday, Orban told them negotiations should be concluded by the weekend.
The government proposal now on the table would allow law-enforcement workers to retire early while taxing these pensions taken early, though the pension payment would be raised.
Earlier on Friday police cordoned off a section of the street where the prime minister lives after the unions said on Monday they planned to demonstrate in front of his residence, without specifying a date or time.