On “Meet the Press,” Mayor Michael R. Bloomberg declared, “We have to go and get the immigrants here.” To a group of business leaders in Brooklyn, he extolled “the economic power” of immigration. And in his State of the City address on Wednesday, he interrupted a litany of local issues to urge Americans “to fix our broken immigration system.”

Having taken on the New York City school system and the illegal gun trade, Mr. Bloomberg has now proposed overhauling the federal immigration laws, offering himself as the man to help settle one of the nation’s thorniest debates. He praises immigrants as a precious resource and speaks of current immigration policy with undisguised disgust — “the most ruinous economic policy you could ever conceive of” was his line on Wednesday.

But the stark language often brushes past the complexities surrounding immigration, which has proved to be a nuanced and difficult issue, even for the mayor.

Though Mr. Bloomberg, the grandson of immigrants from Russia and what is now Belarus, has set an inclusive tone in his nine years as mayor and has provided critical services for immigrants, some programs have failed to live up to expectations.

And though he has adopted landmark policies to protect the privacy of illegal immigrants, he has also rankled immigrants’ advocates who say city and police officials work too closely with federal authorities, putting many noncriminals at risk of arrest and deportation.

“Mayor Bloomberg has been an important ally of immigrant communities,” said Andrew Friedman, co-director of Make the Road New York, an advocacy group. “But there are a number of areas where he has not used his power, and as a result, immigrant New Yorkers are more likely to be deported, less likely to learn English, less likely to be paid lawful wages.”

Supporting immigrant causes is virtually a job requirement for any New York mayor, but many immigrants and their supporters say Mr. Bloomberg has gone well beyond the expected. His New York is a city where illegal immigrants start businesses, raise families and attend public school without the constant fear, prevalent in many parts of the country, that they can be deported if a police officer notices them.

The city’s information line, 311, greets callers in Spanish, Russian, Mandarin, Cantonese, Korean and Creole. In his address on Wednesday, the mayor promised new programs to help immigrant entrepreneurs obtain loans and expertise.

Yet even as New York ranks among the American cities most accommodating to newcomers, certain practices keep immigrants on edge. At the city jail complex on Rikers Island, Correction Department officials provide lists of foreign-born inmates to federal officers who then question, detain and deport about 3,200 a year. Immigrants’ advocates say the collaboration leads to the removal of many immigrants who have not been convicted of, or even charged with, serious crimes, and makes others afraid to cooperate with law enforcement.

Mr. Bloomberg’s efforts to make city agencies more accessible to people who speak little or no English have won wide acclaim. In 2003, he signed a law requiring the city’s Human Resources Administration and social service agencies to provide interpreters and other language help; an executive order in 2008 extended that to every agency dealing with the public.

But Legal Services NYC, a nonprofit group, is suing the Human Resources Administration, saying that follow-through has been spotty, leading to “humiliating discrimination” against immigrants. Many city workers remain unaware of the rules, and some are unequipped to help people who speak other languages, lawyers and advocates say.

“There is a big disconnect between what our city policy says and what’s happening,” said Amy S. Taylor, the lawyer who filed the suit.

Mr. Bloomberg said in a recent interview that language access was improving. But, he noted, “you’re never going to have every language spoken in every agency 24 hours a day.”

He said that he had worked to build trust between immigrants and government agencies, and that newcomers were crucial to New York’s success.

“Our lifeblood is a constant stream of new immigrants,” he said, “to improve our cuisine, our culture, our language and, mainly, our economy.”

Mr. Bloomberg began his third term a year ago by announcing plans for a national task force of big-city mayors and prominent business leaders to press Congress for an overhaul of immigration policy. His principal argument was, and is, that immigrants are good for the economy because they open businesses, create jobs and pay taxes.

There is disagreement over how much influence Mr. Bloomberg, an independent, might wield in the national debate over immigration, given the Republicans’ takeover of the House and their chilliness to any thaw in immigration policy. But few doubt his influence in New York, where City Hall officials point to a series of pro-immigrant policies and decisions that they call national models.

“It started when he took office,” said Fatima Shama, commissioner of the city’s Office of Immigrant Affairs. “He was able to focus New Yorkers on being one city, and showing that all New Yorkers matter. From that, we saw a number of policies emerge.”

Chief among them was Executive Order No.41, issued in 2003, which sought to protect crime victims and witnesses from fear of deportation by forbidding city workers to ask immigrants about their legal status.

A similar policy had been in place since the Koch administration, but by the time Mr. Bloomberg took office, a federal challenge and subsequent court decisions had made its renewal uncertain. The Bloomberg administration came up with an approach that broadened the policy and drew no challenges.

Like the earlier measures, however, Mr. Bloomberg’s order made an exception allowing police officers who suspect illegal activity to inquire about immigration status. While there is no evidence that it has led to widespread profiling or harassment, advocates have complained for years, particularly with regard to the Police Department, that there is no mechanism in place to enforce the policy or investigate violations.

Immigrants’ leaders also lament that the mayor has not joined some officials of other municipalities across the country in resisting Secure Communities, a new program that will help federal officials deport illegal immigrants by improving coordination with local police departments.
Mr. Bloomberg said that while he aimed to accommodate immigrants, he was responsible for keeping the city safe. “If people commit crimes, we have an obligation,” he said. “If they broke the law, make them pay the penalty.”

The Bloomberg administration has also sought to solve intractable problems like finding legal representation for immigrants, who are not entitled to court-appointed lawyers in the civil courts, where their immigration violations are heard. City Hall has pledged to provide $2 million to provide lawyers and training, placing New York far ahead of the national norm on the issue, said Robert A. Katzmann, a judge on the United States Court of Appeals for the Second Circuit who has worked closely with the administration.

The mayor has not endorsed every suggested change in immigration policy, particularly when a proposal collides with his pro-business agenda. For example, he resisted calls to support a state bill, signed into law last month by Gov. David A. Paterson, to set stiffer penalties for employers who underpay workers, many of them illegal immigrants; Mr. Bloomberg’s aides say he was concerned about its effect on small businesses.

For many, though, Mr. Bloomberg’s signal mark on the immigration debate had nothing to do with policy. His declaration of support for the planned Islamic community center and mosque near ground zero was a stirring affirmation that the mayor would champion the city’s diversity, advocates said.

“That was a defining moment,” said Chung-Wha Hong, the executive director of the New York Immigration Coalition. “He didn’t really have to do that. He got there because of the connections and the work he’s done and his whole philosophy on immigration.”

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