WASHINGTON — The Supreme Court on Thursday agreed to hear a challenge to a federal campaign finance law brought by Senator Ted Cruz, Republican of Texas, and a dispute over whether Boston must allow a private group to raise a flag bearing a cross in front of its City Hall.

The campaign finance law case concerns a federal law that places a $250,000 limit on the repayment of personal loans to campaigns using money from postelection donations. Seeking to test the constitutionality of the law, Mr. Cruz lent $260,000 to his 2018 re-election campaign.

The law does allow repayments of loans of more than $250,000 so long as campaigns use pre-election donations and make the repayments within 20 days of the election. But the campaign did not repay Mr. Cruz by that deadline, so he stands to lose $10,000.

Mr. Cruz sued the Federal Election Commission before a special three-judge district court in Washington, arguing that the repayment cap violated the First Amendment.

Judge Neomi Rao, who ordinarily sits on the U.S. Court of Appeals for the District of Columbia Circuit, wrote for a unanimous panel that the cap amounted to an unconstitutional burden on candidates’ free speech rights.

“Protections for political speech extend to campaign financing because effective speech requires spending money,” Judge Rao wrote, adding that “the loan-repayment limit intrudes on fundamental rights of speech and association without serving a substantial government interest.”

In the Biden administration’s Supreme Court brief, Elizabeth B. Prelogar, then the acting solicitor general, noted that Mr. Cruz’s campaign had more than $2 million on hand after the election and could have lawfully repaid him from those funds so long as it did so within 20 days. His injury, she wrote, was self-inflicted.

In any event, Ms. Prelogar wrote, the repayment cap was lawful.

“The loan-repayment limit imposes at most a modest burden on First Amendment rights,” she wrote. “It does not limit the amount of money that a candidate may spend, the amount of money that a campaign may borrow, the amount of money that a candidate may raise or the amount of money that a donor may contribute to a campaign.”

Postelection donations that can directly benefit a successful candidate, she wrote, are different in kind from contributions during an election. “A postelection contribution is thus more likely than a pre-election contribution to be motivated by an expectation of special favors from the recipient,” she wrote.

Mr. Cruz’s lawyers responded that the campaign owed more money than it had on hand on Election Day and that it was entitled to pay vendors rather than repay Mr. Cruz from pre-election contributions.

“Cruz has a First Amendment right to loan money to his campaign free from governmental restrictions as to amount and time of repayment,” the senator’s lawyers wrote in their brief in the case, Federal Election Commission v. Ted Cruz for Senate, No. 21-12. “That Cruz could have avoided his $10,000 loss by refusing to loan his campaign more than $250,000, or by requiring repayment in full within 20 days, does not change the fact that he suffered a $10,000 injury by exercising his constitutional right to make the loan that he did.”

The Supreme Court also agreed on Thursday to decide whether Boston was entitled to turn down a request to raise a flag bearing a Christian cross on one of the three flagpoles in front of its City Hall. That flagpole, which ordinarily flies the city’s flag, is occasionally replaced by a different one for a limited time after an approval process.

In a 12-year period ending in 2017, “the city approved 284 flag-raising events that implicated its third flagpole,” according to a unanimous three-judge panel of the U.S. Court of Appeals for the First Circuit, in Boston.

“These events,” Judge Bruce M. Selya wrote, “were in connection with ethnic and other cultural celebrations, the arrival of dignitaries from other countries, the commemoration of historic events in other countries and the celebration of certain causes” like gay pride.

In 2017, the city rejected a request from Camp Constitution — a group that says it seeks “to enhance understanding of the country’s Judeo-Christian moral heritage” — which said it sought to raise a “Christian flag” at an event that included “short speeches by some local clergy focusing on Boston’s history.”

The group sued, saying the city’s decision violated, among other things, its right to free speech. The appeals court ruled for the city, largely on the ground that the government is entitled to choose the messages it endorses.

“The city has never before displayed such a flag and, as such, this pioneering elevation of an ‘important symbol’ of the Christian heritage would come without the secular context or importance that the passage of time may have afforded other displays,” Judge Selya wrote. “The raising of the Christian flag thus would threaten to communicate and endorse a purely religious message on behalf of the city.”

In its brief asking the justices to review the case, Harold Shurtleff and Camp Constitution v. City of Boston, No. 20-1800, the group said the appeals court had used the wrong First Amendment analysis. The flagpole is a public forum, the brief said, and the city is not entitled to discriminate against religious messages in such a forum.