As a high-profile strike by University workers entered its fourth week, Yale and its unions appeared close to a settlement Wednesday night after both sides reported progress on a number of contentious issues.

Yale President Richard Levin and John Wilhelm ’67, president of the parent union of locals 34 and 35, met with New Haven Mayor John DeStefano Jr. until 11:30 p.m. Wednesday, after a full evening of discussions. Leaders will reconvene for talks today, possibly bringing to an end the three-week-long strike by members of locals 34 and 35. Based on discussions with union representatives, several rank-and-file workers said Wednesday they expected the strike to end this week and hoped to return to work Monday.

Negotiators reached tentative agreements on job security and subcontracting issues earlier this week, union leaders said. The agreements are considered tentative until final contracts are signed.

After their meeting with Yale negotiators Wednesday afternoon, union leaders said four major components of the contracts remain unresolved: wages, pensions, retroactivity and the duration of the contracts.

After leaving DeStefano’s office late Wednesday night, Levin characterized the talks as progressing, but not finished.

“We’re still working. We’re not done yet, but we’re still making progress,” Levin said. “It’s tough putting all the pieces together. We just haven’t gotten them all together.”

Wilhelm offered a similar progress report.

“We’re working at it,” he said while leaving City Hall.

Levin and Wilhelm met with DeStefano following an afternoon two and half hour meeting between both negotiating teams. Local 35 President Bob Proto said the afternoon meeting was informal, focusing on “rebuilding [the] relationship” between Yale and its unions, rather than on contract numbers.

DeStefano returned early from a trip to the Midwest to meet with the two sides Wednesday afternoon. The mayor, who is president of the National League of Cities, had been scheduled to attend a conference in Illinois today.

Several union members said they expect the strike will end this week.

“I heard they’re close, that they’re hoping to have things wrapped up by the end of the week,” Local 34 member Theresa MacCalmon said while picketing outside the Hall of Graduate Studies Wednesday.

MacCalmon said Local 35 has secured the rights to work in several newly renovated buildings, including Sprague Hall, Vanderbilt Hall and the Congress Avenue Building at the School of Medicine. In recent weeks, local and state leaders have lambasted Yale for hiring subcontracted laborers.

But many striking union members said the two sides have clashed on the duration of the contract. Picketers said the University has offered an eight-year contract, while the unions are proposing a six-year agreement.

The discussions between Levin and Wilhelm followed several recent events in which the national union leader criticized the University. Earlier Wednesday, Wilhelm led a march from the Omni Hotel — where the Connecticut AFL-CIO is holding a convention — to Beinecke Plaza. As the union supporters marched towards Woodbridge Hall, they held a banner reading “Yale: Settle.”

The Rev. Scott Marks, who has emceed at recent union demonstrations, said at Wednesday’s rally that he anticipated the two sides would settle Wednesday evening.

Proto said it has been helpful that top University officials have been present at recent talks. Earlier this year, union leaders criticized Levin and other key decision-makers for not attending bargaining sessions.

“It’s absolutely positive having President Levin coming to the table,” Proto said.

— Staff reporters Jessica Feinstein, Philip Rucker, Will Sullivan and Stephanie Teng contributed to this report.