Image copyright AP Image caption New York City Mayor Bill de Blasio emerges from Trump Tower

New York's mayor says he has told US President-elect Donald Trump people in the city are "fearful" of what his White House administration could bring.

During a meeting at Trump Tower, Bill de Blasio said he warned the Republican he would aim to shield undocumented immigrants from deportation.

He said Mr Trump's plans would not work in "the ultimate city of immigrants".

Mr Trump wants to deport or jail up to three million undocumented immigrants who he says have criminal records.

This figure is much disputed. The Migration Policy Institute, a nonpartisan think tank, estimates there are actually about 820,000 undocumented immigrants with criminal records, including many whose only conviction is for crossing the border illegally.

Mr de Blasio is not the only city leader to oppose the incoming US president's immigration policies.

Media playback is unsupported on your device Media caption Trump's name removed from NYC buildings

The mayors of Los Angeles, San Francisco, Chicago, Boston, Philadelphia and Washington DC have also vowed to protect their immigrant residents from deportation.

In other developments:

Turkish President Recep Tayyip Erdogan has rebuked anti-Trump protesters in the US, saying: "Hold on a second. The election process just ended, show some respect! How will he govern, let's see that first"

House Democrats sent a letter to Mr Trump calling on him to rescind the appointment of Breitbart News executive Steve Bannon as his chief strategist, after critics accused him of peddling white nationalist hate

The president of the Czech Republic said he hopes Mr Trump's ex-wife, Ivana, will become the new US ambassador after the socialite expressed interest in taking up the post in her Eastern European motherland

Mr De Blasio vowed after Mr Trump's election victory to delete the names of undocumented workers from a city database to prevent them from being rounded up.

The New York mayor, a liberal Democrat, told reporters his hour-long meeting with Mr Trump had been "respectful" and "candid".

Media playback is unsupported on your device Media caption Trump election: Family divided over Trump rhetoric

"I reiterated to him that this city and so many cities around the country will do all we can to protect our residents and to make sure that families are not torn apart," he told reporters.

He added that New York - home to nearly three times the national average of foreign born citizens - "has succeeded because it was open for everyone, the place built of generation after generation of immigrants".

But Mr de Blasio also said Mr Trump "loves" his hometown, which voted by a large margin for the Democratic candidate, Hillary Clinton.

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As they met, Mr Trump's name was being removed from three buildings in New York City following a petition by residents who opposed his election.

Workers on an elevated platform took down his moniker, one gold letter at a time, from the apartment blocks on the west side.

But his flagship Manhattan tower, where the Republican has been holed up preparing for his January inauguration as the nation's 45th president, was not affected.

On Wednesday, he criticised claims of disarray in his transition, singling out the New York Times for reporting that world leaders have had trouble contacting him.

Image caption US President Barack Obama said in Greece that he and Mr Trump "could not be more different"

The property mogul tweeted that he had taken calls from many foreign leaders, adding: "@nytimes is just upset that they looked like fools in their coverage of me."

Mr Trump and Vice President-elect Mike Pence have spoken with 29 world leaders since the election, according to a statement from the transition team.

Japanese Prime Minister Shinzo Abe will be the first foreign leader to meet the new US president-elect, in New York on Thursday.

Media playback is unsupported on your device Media caption Senior Republican strategist Mike Duhaime explains to Radio 4's Today the nature of Trump's transition to the White House.

Meanwhile, current US President Barack Obama continued his farewell foreign trip, acknowledging in Greece that he and Mr Trump "could not be more different".

As he toured Athens, birthplace of democracy, Mr Obama added: "As long as we retain our faith in the people, as long as we don't waver from those central principles that ensure a lively, open debate, then our future will be ok."