Washington (AFP) - President Donald Trump vowed to improve floundering ties with Russia, while also reassuring close US allies he supports NATO.
Trump faced a first legal defeat amid growing international alarm over his halt to refugees and travelers from certain Muslim majority countries, with a federal judge blocking part of the ban.
The temporary stay orders authorities to stop deporting dozens of refugees and other travelers who had been detained at US airports since Trump signed his measure Friday afternoon.
British Prime Minister Theresa May indicated she does "not agree" with the restrictions, and will intervene if they affect UK nationals.
French President Francois Hollande warned of the "economic and political consequences" of the American leader's protectionist stance.
Iran's Foreign Minister Mohammad Javad Zarif said Sunday that Trump's decision to ban arrivals was "a great gift to extremists".
"#MuslimBan will be recorded in history as a great gift to extremists and their supporters," Zarif said as part of a string of tweets.
"Collective discrimination aids terrorist recruitment by deepening fault-lines exploited by extremist demagogues to swell their ranks."
Yemen's Huthi rebels also slammed the ban, saying any attempt to classify Yemen and its citizens as a probable source for terrorism "is illegal and illegitimate."
Trump's sweeping executive order suspends the arrival of refugees for at least 120 days and bars visas for travelers from seven Muslim majority countries for the next three months.
The move sparked large protests at major airports across the country. At New York's John F. Kennedy International Airport, some of the 2,000 demonstrators chanted "Let them in, let them in!"
- Better US-Russia ties? -
Trump's friendly stance toward Putin, whom France and Germany accuse of seeking to undermine Western unity, is being scrutinized since he won the US election in November.
The White House hailed the call with Putin as a "significant start" to better US-Russia ties, while the Kremlin said the pair agreed to develop relations "as equals" and to establish "real coordination" against the Islamic State group.
Trump took office last week with US-Russia relations at new Cold War-level lows amid accusations by American intelligence agencies that the Kremlin hacked Democratic Party emails as part of a pro-Trump campaign to influence November's election.
The president -- who has raised the prospect of easing sanctions imposed against Russia after its annexation of Ukraine's Crimean Peninsula in 2014 -- has cast doubt on whether Russia meddled in the election.
In a flurry of calls that began early in the morning and rounded out an already frantically paced week, Trump spoke with Japanese Prime Minister Shinzo Abe, German Chancellor Angela Merkel, Putin, Hollande and Australian Prime Minister Malcolm Turnbull.
The conversations gave the US president an early opportunity to explain new policies that have baffled and unnerved much of the rest of the world -- particularly his order to temporarily halt all refugee arrivals and those of travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
European leaders are also concerned about Trump's virulent criticism of NATO -- he has dubbed the transatlantic military alliance "obsolete" -- at a time when it stands as the main defense against Putin.
But in his call with Merkel, Trump agreed on NATO's "fundamental importance," the White House said.
The United States provides significant funding to NATO, and Trump has urged other member nations to step up their contributions.
- 'Extreme vetting' -
Trump's pronouncement on Muslim immigration makes good on one of his most controversial campaign promises to subject travelers from Islamic countries to "extreme vetting," which he declared would make America safe from "radical Islamic terrorists."
"It's not a Muslim ban," Trump insisted.
"It's working out very nicely. You see it at the airports, you see it all over," he told reporters.
The new protocols specifically bar Syrian refugees from the United States indefinitely, or until the president himself decides that they no longer pose a threat.
The legal challenge, which won a first battle in US District Court in New York, was filed by the American Civil Liberties Union and other advocacy groups after two Iraqi men were detained late Friday at JFK.
- 'Greatest nation' -
One of the men, Hameed Khalid Darweesh, had worked for the US government in Iraq for 10 years.
"America is the greatest nation, the greatest people in the world," Darweesh said after his release.
Mark Doss, a supervising attorney at the International Refugee Project at the Urban Justice Center, said Darweesh's detention and release showed the new policy was being implemented "with no guidance."
The ban has also triggered a political backlash.
"To my colleagues: don't ever again lecture me on American moral leadership if you chose to be silent today," Connecticut Senator Chris Murphy, a Democrat, tweeted late Friday.
His tweet was accompanied by the now iconic photograph of Aylan Kurdi, a three-year-old Syrian boy whose body washed up on a beach in Turkey in 2015 after a failed attempt to flee Syria's brutal war to join relatives in Canada.
International groups and civil liberties organizations have roundly condemned Trump's orders.
"'Extreme vetting' is just a euphemism for discriminating against Muslims," said ACLU executive director Anthony Romero.
Romero said Trump's order breached the US constitution's ban on religious discrimination by choosing countries with Muslim majorities for tougher treatment.
Iran answered in kind by saying it would ban Americans from entering the country, calling Trump's action insulting.
But the US leader did get backing from Czech President Milos Zeman, who praised him for being "concerned with the safety of his citizens."