Trump's latest broadside showed his frustration with stalled ceasefire talks and comes two days after he called the Kremlin leader “absolutely CRAZY” following a major drone attack on Ukraine.
Diplomatic efforts to end the war have intensified in recent weeks, but Putin has been accused of stalling peace talks.
Trump did not specify what the “really bad” things were.
Trump told reporters on Sunday he was “absolutely” weighing such a move.
The White House said Trump was keeping “all options” open.
Biden, Trump's Democratic predecessor, imposed sweeping sanctions after Russia's invasion. Trump has so far avoided what he says could be “devastating” sanctions on Russian banks.
His frustration at his failure to end a war he said he could solve within 24 hours boiled over at the weekend after Russia's drone barrage killed at least 13 people.
Russia has kept up attacks despite a phone call eight days ago in which Trump said Putin had agreed to immediately start talks.
“Kyiv, with the support of some European countries, has taken a series of provocative steps to thwart negotiations initiated by Russia,“ the Russian defense ministry said.
Fresh drone attacks were also reported overnight to Wednesday.
'Eternal waiting'
“We need to end this eternal waiting -- Russia needs more sanctions,“ Ukrainian President Volodymyr Zelensky’s chief of staff Andriy Yermak said Tuesday on Telegram.
Veteran Republican Senator Chuck Grassley called for strong measures to let Putin know it was “game over.”
Trump's Ukraine envoy Keith Kellogg told Fox News that the next peace talks between Russia and Ukraine, if they happen, would likely take place in Geneva after Moscow rejected the Vatican as a venue.
The Swiss government would not confirm that it would host the talks.
Russia and Ukraine held their first direct talks in more than three years in Istanbul in early May.
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