British Prime Minister Theresa May's meeting to discuss Brexit with her Irish counterpart, Enda Kenny, on Monday had its spotlight squarely stolen by the mounting global reaction against U.S. President Donald Trump's order restricting travel from seven Muslim-majority countries.

During the press conference immediately following the bilateral meeting, Irish Prime Minister Kenny delivered a considerably cleaner refutation of the newly installed U.S. government's highly controversial travel policy than did the U.K.'s May.

However, both leaders emphasized that the will of democratic Americans had to be respected at this time.

"Whatever you think of the American President, this is a man who's elected now by votes of the American people, who is now implementing what he said he would do for the last two years," Kenny said to reporters.

"I don't agree with this particular policy and I will give my reasons for that when I talk to him but in respect of our own connections with the United States, I think it's important to keep that contact very much alive, more so now than ever before," he added.

May continued to tiptoe around growing calls from her citizens to provide an outright criticism of the policy, instead restricting her commentary to indirect observations about variations in style between her country and the U.S.