McCain, a senior Republican senator from Arizona and a regular critic of Trump as well as Russia, sent a letter to the president in which he urged him to provide lethal aid to Kyiv.
"That this surge of attacks began the day after [Putin] talked with you by phone is a clear indication that Vladimir Putin is moving quickly to test you as commander in chief. America's response will have lasting consequences," McCain said in the letter released by his office.
Trump has repeatedly expressed hope for improved relations with Moscow.
In Brussels, EU President Donald Tusk urged Russia to use its influence to "disengage the Russia-backed separatists" and to restore a cease-fire.
The Ukrainian military reported two soldiers killed overnight on February 2 and 10 wounded in shelling in the government-held town of Avdiyivka, just north of the separatist stronghold of Donetsk. The separatists said one of their fighters was killed.
"Moscow was putting Avdiyivka on the brink of a humanitarian catastrophe," Poroshenko's statement said.
More than 9,750 people have been killed since the conflict in eastern Ukraine erupted in April 2014.