WASHINGTON — The Supreme Court’s new term began Monday with no cross words between the justices, although a steady stream of divisive social issues awaits them in the coming months.

In their first public meeting since a number of high-profile decisions in June displayed passionate, sometimes barbed disagreement, the justices were deferential to each other even as they engaged in typically aggressive questioning of lawyers.

The court also rejected hundreds of appeals that piled up over the summer, including one from the Obama administration that claimed it will have a much tougher time prosecuting insider-trading cases because of a lower court ruling from New York. San Jose, California, also lost its bid to lure the Athletics from Oakland over the objection of Major League Baseball.

Without comment, the high court left in place a decision by the federal appeals court in New York last year that threw out the insider trading convictions of two high-profile hedge fund managers. The federal government’s pursuit of insider trading on Wall Street resulted in more than 80 arrests and 70 convictions over several years.

Just after 10 a.m., Chief Justice John Roberts formally closed the previous term, most notable for its decision extending same-sex marriage nationwide, and began the new one.

As often happens, 82-year-old Ruth Bader Ginsburg was the first justice to speak in a case that involves a California woman who lost her legs after she fell while attempting to board a train in Austria. The issue is whether she can sue the state-owned Austrian railway in U.S. courts.

Ginsburg sounded skeptical that the lawsuit could proceed. “There is one contact with the United States. A pass is bought from a travel agent in Massachusetts, a pass covering 30-odd railroads. That’s all that happened in the United States,” Ginsburg said.

All the other justices, except Clarence Thomas, eventually joined in the questioning and most seemed to agree with Ginsburg.

Consensus almost certainly will give way to division when the court takes up cases later this term that deal with abortion, religious objections to birth control, race in college admissions and the power of public-sector unions. Cases on immigration and state restrictions on voting also could make it to the court in the next nine months.

The term will play out against the backdrop of the presidential campaign, in which some candidates are talking pointedly about the justices and the prospect of replacing some of them in the next few years. Four justices are in their 80s or late 70s, led by Ginsburg.