Shannon Farmer, chief negotiator for the administration, declined to characterize the discussions, saying she was waiting to see a written proposal from the union.
Both sides said they expected to get together again early next week.
The discussions took place in the ballroom of the Radisson Blu Warwick Hotel at 17th and Locust Streets, with tables put together to form a massive rectangle and 48 chairs to accommodate representatives of the D.C. 33 locals and the city's 12-person negotiating team.
The city's negotiators shuttled in and out of the meeting room four times, leaving for long periods while the union representatives discussed the situation among themselves.
Among pending issues, the city is seeking authority to furlough workers for up to three weeks annually if necessary to balance the budget, a power opposed by the union.
The city wants to limit overtime pay to situations in which the employee is working more than 40 hours a week, not counting holidays or sick time.
And it wants to put newly hired workers into a hybrid pension plan, with a lower level of guaranteed benefits and a supplemental account such as a 401(k).
Matthews said the union was looking for wage increases of about 3 percent annually, with back pay, going back to the end of the last contract.
The city's most recent offer - the focus of a Common Pleas Court lawsuit seeking permission to impose contract terms on union members - would raise wages about 4.5 percent and provide no back pay.