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Harvard and its graduate students union could not reach agreements on compensation, health benefits, and grievance procedures during a bargaining session Friday, with just over a week remaining before the union plans to strike if no agreement is reached.

Harvard Graduate Students Union-United Automobile Workers brought a new compensation proposal to the table, while Harvard presented revised versions of its compensation and health benefits proposals. Neither side offered changes to their sexual harassment and discrimination grievance procedure proposal. The two committees did agree on one provision — job postings.

Under the agreement, the University would create a central website for open positions included in the bargaining unit. The postings would include the pay rate, expected work schedule, and disclose that the position is covered by HGSU’s contract.

The next bargaining session is scheduled for Tuesday and is the last scheduled bargaining session before the union’s Dec. 3 strike deadline. HGSU has vowed to initiate a strike if a contract is not reached by then. The union indicated it would strike indefinitely in a tweet last Wednesday.

In the meantime, the union has called for scheduling additional bargaining dates.

“We’re ready to bargain any time between now and December 3. It’s up to them to join us,” wrote union bargaining committee member Justin Bloesch in an email update to HGSU members.

University spokesperson Jonathan L. Swain declined to comment on whether University negotiators would schedule additional bargaining sessions.

On Friday, HGSU also offered counterproposals on union security and tuition and fees, according to Bloesch. The union had not updated their proposals on their website as of Sunday evening.

Harvard’s updated compensation proposal — posted to a website devoted to union negotiations — clarified pay rates for student teaching fellows, but did not commit to increased pay compared to previous versions. The University also raised its pool funds supporting health insurance premiums, dental health plan, and child care by $25,000 each.

Ahead of the meeting, bargaining committee member Cole M. Meisenhelder wrote that others planned to attend to “pressure the administration to agree to a fair contract” in an email update to members last Wednesday.

Swain wrote in an emailed statement that roughly 30 union members attended the session Friday. The bargaining committee has 10 members.

“The University and HGSU continue to engage on the key issues that are the focus of these negotiations and we look forward to continued progress,” Swain wrote.

HGSU did not respond to a request for comment.

Before heading to Friday’s bargaining session, HGSU members also delivered letters from politicians supporting their cause to University President Lawrence S. Bacow’s office.

Among the letters was one from all 11 members of Massachusetts’ Democratic congressional delegation including Senators Elizabeth Warren (D-Mass.) and Edward J. Markey (D-Mass.), as well as United States Representatives Ayanna S. Pressley (D-Mass.), Joseph P. Kennedy III (D-Mass.), and Seth W. Moulton ’01 (D-Mass.).

“We believe this strike would be detrimental to students, workers, and community members and we therefore urge you to engage in good faith effort to reach a fair agreement before the strike deadline,” they wrote. “Your decision to bargain has set Harvard apart from many other institutions of higher education, and we ask that you continue to set the bar by negotiating a first contract that will ensure fair treatment and strong workplace protections for workers, as well as uninterrupted education for your students.”

Bacow plans to respond to the letter, according to Swain.

—Staff writer James S. Bikales can be reached at james.bikales@thecrimson.com. Follow him on Twitter @jamepdx.

—Staff writer Ruoqi Zhang can be reached at ruoqi.zhang@thecrimson.com. Follow him on Twitter @RuoqiZhang3.