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NEW DELHI— ­ A diplomatic tiff between India and Italy showed no signs of easing Monday after India’s Supreme Court extended its travel restrictions against the Italian ambassador for another week.

A lawyer for Ambassador Daniele Mancini pleaded in a hearing Monday that his client enjoys diplomatic immunity that protects him against arrest or detention. But according to local news reports, justices on the court verbally rejected that argument.

The standoff between the countries has been brewing for a year after two Italian marines shot and killed two Indian fisherman they had mistaken for pirates. Italy claims the events took place in international waters, while the Indian authorities have responded that they took place in Indian waters off the southern state of Kerala.

The two marines, who always appear impeccably dressed and groomed and wearing stylish sunglasses, surrendered last year to the Indian authorities and went to jail. They were allowed to return home for the Christmas holidays, after which they returned to India and went back to jail.

Most recently, Mr. Mancini asked for permission for the men to return to Italy for four weeks to vote in that country’s elections, and he signed an affidavit promising that they would return.

Last week, Mr. Mancini formally reneged on that promise, saying the marines would not return. In response, the Indian Supreme Court issued an alert to airports barring Mr. Mancini from leaving the country.

The question is whether Mr. Mancini surrendered his diplomatic immunity in the matter when he filed his affidavit promising the marines’ return, as he may very well have. But Indian officials have so far declined to say how they would respond if Mr. Mancini appeared at an airport seeking to leave the country. Arresting or detaining the ambassador would be a highly unusual step.

Relations between Italy and India have been strained for other reasons, including a growing furor over alleged bribes paid to Indian military officials by officials of the Italian conglomerate Finmeccanica to win a contract to provide high-end helicopters. Indian officials repeatedly claimed to have gotten little cooperation from the Italian authorities in their investigations of the alleged bribes. Silvio Berlusconi, a former Italian prime minister, has defended bribes as necessary “when you are negotiating with third world countries and regimes,” hardly a ringing endorsement of the Indian government.

An added part of the embarrassment for both sides is that Italy is the birthplace of India’s most powerful woman, Sonia Gandhi, president of the Indian National Congress party. Mrs. Gandhi rarely likes to mention her foreign origins, so any scandal involving Italy is embarrassing for her, never mind two such scandals.