Russian troops appear close to driving Ukraine from all the territory it seized in the Kursk region of Russia last year, a prospect that President Trump appeared to acknowledge in a social media post on Friday.

Later in the day, President Vladimir V. Putin of Russia insisted that Ukraine order some of its forces in Kursk to surrender.

The Russian push in Kursk appeared to accelerate after Mr. Trump froze military aid and intelligence support to Ukraine on March 3. The flow of aid resumed this week as Ukraine agreed to a Trump administration proposal for a 30-day cease-fire with Russia.

On Thursday, Mr. Putin said he was open to the proposal but would seek to negotiate over a number of issues.

Both Mr. Putin and Mr. Trump claimed on Friday that Ukrainian forces were surrounded in Kursk, where Kyiv’s troops stunned Russia with a cross-border incursion last summer.