Oil and gas are Russia's biggest exports. The two Russian oil firms export 3.1 million barrels of oil per day. Rosneft is responsible for nearly half of all Russian oil production, which makes up 6% of the global output, according to UK government estimates.
Moscow's biggest customers include China, India and Turkey. Trump has also urged these countries to halt purchases of Russian oil in a bid to put economic pressure on the Kremlin.
India is poised to sharply reduce Russian oil imports in light of Trump's announcement, news agency Reuters reports, citing unnamed industry sources. China has said it opposes the US sanctions.
Ukraine has in recent months targeted Russian oil refineries and energy infrastructure in an attempt to hurt its economy.
Zelensky had visited the White House on Friday, seeking to acquire long-range Tomahawk missiles that could strike deep into Russian territory, but came away empty-handed.
The day before, Trump had announced the proposal to meet Putin in Hungary after an unscheduled call from the Russian leader.
But following a call between US Secretary of State Marco Rubio and his Russian counterpart Sergei Lavrov, the idea was put on hold, with Trump saying he didn't want a "wasted meeting".
Trump later said he had refused to give Ukraine the missiles as they were "highly complex" and took a year of intense training to use. Zelensky appeared to suggest that, like with the sanctions, Trump may change his mind in the future.
Fighting on the ground continued overnight, with strikes on Ukraine's capital, Kyiv, killing at least two people, officials said.
Earlier on Wednesday, Russia unleashed an intense bombardment that killed at least seven people, including children.