Hundreds of Harvard graduate students walked out of class and off the job Tuesday, kicking off their first strike after contract negotiations with the university stalled.

Students marched for hours down snow-covered sidewalks around Harvard Yard, carrying signs, banging on empty plastic cans, and chanting “What do we want? Contract! What do we do if we don’t get it? Shut it down!’’

“The things we’re asking for . . . it would be really easy for Harvard to provide,’’ said Sophie Wilkowske, 24, a graduate student in history. “We’re going to stay out here until they do.’’

The graduate students were joined on the picket line by some professors and undergraduate students.

David Carey, a sophomore, walked out with his Spanish class to support his teaching assistants. At Harvard, much of the learning happens in small groups led by graduate students, Carey said.

“They have certain rights that they need to have protected,’’ Carey said.

The strike comes after more than a year of negotiations between the newly formed graduate student workers union and Harvard officials.

Harvard officials have said that a strike is “unwarranted’’ and will not help resolve disagreements over the contract.

Still, the graduate students, who teach classes, grade papers, and work in research labs, said they want to send Harvard administrators a message that their labor is valuable and that they should be compensated fairly and offered more protections against sexual harassment and discrimination.

Caroline Keroack, 27, a doctoral student in biosciences, said she is still waiting for Harvard to pay her for a class she helped teach last spring. Because she is in the sciences, Keroack said she earns a reasonable annual stipend — about $38,000 — that helps offset the rent for her one-bedroom apartment in Brighton, but she also works as a teaching assistant to help pay for additional medical expenses, or for eating out.

“I just had my appendix out and had medical expenses that were unexpected,’’ Keroack said. “It would be nice to have the teaching assistant check. . . . It’s hard to set up a monthly budget.’’

Inconsistent paychecks and uncertainty about how many hours they are likely to work each semester as teaching assistants are frequent problems, said graduate student workers. When returns on Harvard’s $40 billion endowment are disappointing, graduate students are often the ones who bear the brunt, receiving the lowest pay increases on campus. Graduate student workers complained that their lives and their pocketbooks are often left to the whims of Harvard’s administrators.

“It’s bonkers,’’ said an international doctoral student in his third year at Harvard, who declined to give his name, because he was concerned about being identified by his department.

The two sides have made tentative progress toward an agreement over training, travel, and support for international graduate students, but remain divided on several major issues, including pay packages and grievance procedures for sexual harassment complaints.

The union is seeking better pay, expanded health care and child care benefits, and an outside arbitrator to handle complaints of sexual harassment, discrimination, and retaliation.

Stipends for Harvard doctoral students vary by school and range from $35,500 to $43,000 annually.

Harvard has proposed an 8 percent pay increase over three years for a majority of the graduate students in the union. But union members said that would end up being less than the 3 percent annual raise many of them have received in recent years.

The union has countered with a proposal for a 5 percent raise in the first year of the contract and a 3.5 percent increase in subsequent years, according to union representatives. Under the union proposal, the first raise would be retroactive to July 1, 2019, and would supplement the 3 percent raise Harvard gave graduate students at the time.

Graduate student workers have also argued that they need to have an independent third party review sexual harassment and discrimination complaints, because Harvard has historically been slow to address such ­allegations against longtime professors. But Harvard officials said the Title IX sexual harassment complaint process has improved significantly in recent years.

While other unions on campus have the option to enter arbitration over sexual harassment complaints, none have used that process, instead choosing to go through the university’s Title IX office, Harvard officials said.

But Harvard administrators have acknowledged that issues of bullying and nonsexual discrimination remain a problem and plan to have a committee that includes graduate students consider ways to address those issues.

Whether the strike will force Harvard to offer more concessions remains unclear, as does the broader impact of the job stoppage.

Some graduate students said they won’t be holding tutoring sessions for undergraduate who are preparing for semester-end exams. Others also said they plan to sit out grading papers and tests.

Keroack, for example, said during the strike she will focus on her own research but avoid the work she usually does as one of the laboratory’s safety officers. Keroack said that she frequently walks through the lab, checking to make sure dangerous materials have not been left out, that the eye washes and showers work properly, and that the chemicals are correctly stored.

Graduate students do many of these day-to-day chores, on top of their research, she said.

“It is a significant amount of work,’’ Keroack said.

It is unclear how long this strike will last. Most university strikes end within two weeks, but Harvard graduate student workers have called for an indefinite work stoppage.

Deirdre Fernandes­ can be reached at deirdre.fernandes@globe.com. Follow her on Twitter @fernandesglobe.