Trump said in a tweet Thursday morning that Gov. Kate Brown, "isn't doing her job."
"She must clear out, and in some cases arrest, the Anarchists & Agitators in Portland," Trump said. "If she can’t do it, the Federal Government will do it for her. We will not be leaving until there is safety!"
In an interview with ABC News Live Wednesday, Brown outlined what appears to be a different understanding of the agreement reached with the Department of Homeland Security -- which would see officers from the Oregon State Police take the place of federal officials protecting the Hatfield Federal Courthouse that has faced attacks and vandalism in recent weeks.
"The plan is very, very clear and both sides are in agreement that starting tomorrow afternoon, Thursday afternoon, Customs and Border Patrol and ICE officers that have been on the streets of Portland will begin leaving," Brown said. "This is definitely a step by step, gradual process, but we know how it is, they will be out of the city of Portland and Oregonians will be in charge."
Brown further argued that the surge of federal forces in the city was part of "a political strategy" by the Trump administration.
"Their presence here was like pouring gasoline on the fire, and their strategy -- because it was a political one, has backfired," Brown said. "And they are leaving they're leaving the streets of Portland and leaving Oregon."
Acting DHS secretary Chad Wolf by contrast released a separate statement following Brown's initial announcement that hinged any withdrawal of federal officers on a clear restoration of peace in the city and near federal properties.
"The Department will continue to maintain our current, augmented federal law enforcement personnel in Portland until we are assured that the Hatfield Federal Courthouse and other federal properties will no longer be attacked," Wolf said. "The Department will continue to re-evaluate our security posture in Portland, and should circumstances on the ground significantly improve due to the influx of state and local law enforcement, we anticipate the ability to change our force posture, as we do everyday at our other 9,000 federal properties we protect across the country."
"We're not going to [move out] that quickly," Wolf added later in a conference call with reporters.
Brown's office responded to ABC News' request for comment by referring to a tweet from Gov. Brown posted to her account Thursday afternoon, where she stated "today, federal troops are preparing to leave downtown Portland."
According to reports from The Oregonian newspaper, following the announcement on Wednesday about the phased withdrawal, dozens of DHS and CBP agents squared off with protesters in the streets near the federal courthouse in the "largest visible response" from the federal officers yet.
DHS did not immediately respond to a request for comment from ABC News as to whether any officers would be departing the city Thursday or whether officials believed Wednesday night's events amounted to any improvement in terms of safety compared with previous nights.
Wolf told reporters Wednesday that federal officers near the courthouse "have faced assaults with Molotov cocktails, mortar-style commercial grade fireworks accelerants, IEDs and other violent weapons since July 4."
ABC News' Luke Barr contributed to this report.