The July 30 edition is "meant to represent this particular moment in US foreign policy," Time said in a statement.
The coverage comes during a week of upheaval for the administration following a meeting between Trump and Putin and a subsequent news conference in Helsinki.
After returning to Washington on Tuesday, Trump said he misspoke during the conference and accepts the consensus of American intelligence agencies, which have reported that Russia interfered in the 2016 election.
He also said the perpetrators "could be other people also."
For its July 2 cover, Time focused on the administration's "zero tolerance" policy of separating migrant children from their parents entering the country unlawfully.
The cover, which showed an illustration of Trump towering over a crying child, included the text "Welcome to America."
- Los Angeles Times
