Britain published plans this month to unilaterally stop some checks on goods moving to Northern Ireland from the rest of the United Kingdom and challenged the role played by the European Union's court in a new clash with Brussels.
The European Commission in response launched two new legal proceedings against Britain and some of the bloc's officials have warned it could launch a trade war.
Johnson pointed to the breakdown of a power-sharing administration in Northern Ireland as a reason for drafting the legislation, the first step in what could be a months-long process before the bill becomes law.
The Democratic Unionist Party has said it will only move to restore Northern Ireland's regional parliament if the law is passed and complained the checks on goods are too onerous for businesses.
"Generally speaking, I think it's quite interesting that the reaction around the table amongst our friends has been much more muted than I think people were expecting," Johnson told reporters on the way to Rwanda where he is attending a Commonwealth summit.
"That's because, you know, in the end, we don't want to fall out over this. We want a solution."
The new legislation is designed to simplify the rules but has drawn sharp criticism in Brussels and Washington where it is seen by many as an inflammatory move that violates an international treaty.
European Commission vice-president Maros Sefcovic said last week the legislation appeared to be driven by Johnson's attempt to win support with his lawmakers after he narrowly won a confidence vote this month.
"No, no, no, do you really think so? Do you really think that most Conservative MPs or most people in the country are thinking about this problem? They're not," Johnson said.
"This is an issue that is entirely to do with the balance of the political situation in Northern Ireland. And we have to respect that."
(Reporting by Andrew MacAskill; Editing by Nick Macfie)
By Andrew MacAskill