In Germany - which has taken in large numbers of people fleeing the Syrian conflict - Chancellor Angela Merkel says the global fight against terrorism is no excuse for the measures.
A spokesman says the Chancellor expressed her concerns to Mr Trump during a phone call and reminded him that the Geneva Conventions require the international community to shelter war refugees.
In Britain, hundreds of thousands of people have signed a petition calling on the UK to prevent Donald Trump from visiting.
British Prime Minister Theresa May met Mr Trump in Washington on Friday, and the US president accepted an invitation for a state visit to Britain later this year.
Opposition Labour leader Jeremy Corbyn says he shouldn't be allowed in while his immigration bans are in place.
"I am not happy with him coming here until that ban is lifted, quite honestly, because look at what's happening with those countries, how many more is it going to be? And what's going to be the long-term effect on the rest of the world?"
Asked about the US ban during a trip to Turkey, British Prime Minister Theresa May pointed out the United States is responsible for its own refugee policy.
"The United Kingdom is responsible for the United Kingdom's policy on refugees and our policy on refugees is to have a number of voluntary schemes to bring Syrian refugees into the country, particularly those who are most vulnerable, but also to provide significant financial contribution to support refugees in countries surrounding Syria."
Ms May later added that Britain does not agree with the curbs.
The Arab League - whose members include many of the countries included in the ban, along with US allies such as Saudi Arabia, Egypt and Jordan - has expressed deep concern and says the restrictions are unjustified.
Iran, whose nationals are affected by the ban, has vowed to respond in kind but says Americans who already hold Iranian visas can still enter the country.
Iranian Parliament Speaker, Ali Larijani, has labelled the US bans racist and fear-based.
"The visa restriction order revealed the fear of this US administration which is afraid of its own shadow. It also exposed their brutal racist manner that is hidden behind their demagogic veneer that pretend to be pro-democracy and pro-human rights. A country that enjoys powerful security does not make such decisions with fear and anxiety."
The United Nations and rights groups are also criticising the measures.
Amnesty International's Audrey Gaughran is calling for the the ban to be overturned.
"It targets predominantly Muslim countries and, shockingly, it targets refugees - some of the most vulnerable people in the world, at a time when we have a global refugee crisis. President Trump has barred all Syrian refugees and has put a hold on the resettlement of refugees in the United States. This executive order is staggering it its scope, deeply shocking and should be reversed immediately."
Australia's Department of Foreign Affairs of Trade says Australians who hold passports from one of the seven countries implicated by the Trump administration temporary immigration ban may be affected.
DFAT says officials are talking to their US counterparts to get clarity on how the ban may affect dual nationals.
Foreign Minister Julie Bishop has spoken from Los Angeles.
"I've had two very constructive conversations now over the past two days with Vice President Mike Pence and he reiterated the significance of the Australia-US relationship. He was very well-briefed on all of the details US-Australia alliance and I am confident that we will continue to build our alliance. It will continue to go from strength to strength."
Labor's Deputy Leader, Tanya Plibersek, says a government's policies must never be based on discrimination.
"We are stronger as a nation when we are united, when we fight discrimination. Of course any country has the right to do backaground checks, to be careful and vcautious about who it invites to become a permanent resident or a citizen, but discrimination based on religion or ethnicity or country of origin has never served us well."
Australia in the past had a "White Australia" immigration policy, which had been abandoned by both major political parties by 1965.
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