Ukrainian President Volodymyr Zelenskyy on Thursday and Friday called on European and NATO leaders by name to exact harsher sanctions on Russia as President Vladimir Putin's forces push deeper toward Ukraine's capital of Kyiv.

Zelenskyy said Friday he held calls with UK Prime Minister Boris Johnson, Finland President Sauli Niinistö, European Commission President Ursula von der Leyen and Canadian Prime Minister Justin Trudeau and pleaded for additional help. 

"Today [Ukraine] needs the support of partners more than ever," Zelenskyy tweeted Friday. "We demand effective counteraction to the Russian Federation. Sanctions must be further strengthened."

"Not all possibilities for sanctions have been exhausted yet," Zelenskyy wrote in a tweet tagging von der Leyen. "The pressure on Russia must increase."

The U.S. has said that more sanctions, including some targeting Putin himself, are on the table. 

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Zelenskyy's push comes after the United States and many European countries slapped Russia with sanctions Thursday as a punishment for its war against Ukraine. But the sanctions largely left Russia's key energy industry untouched. And President Biden notably did not move to remove Russia from the international SWIFT banking system. 

Biden told reporters that he decided against removing Russia from SWIFT because most of Europe opposed such a move at this time. But Zelenskyy implored Western nations to do just that as Russian troops continued to move toward his capital. 

"We demand the disconnection of Russia from SWIFT, the introduction of a no-fly zone over Ukraine and other effective steps to stop the aggressor," Zelenskyy said ahead of a conversation with French President Emmanuel Macron ahead of the European Union's sanctions package Thursday. Neither the E.U. nor the U.S. met those demands. 

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Zekenskyy's exhortations come as Russian forces continue their march toward Ukraine's capital. Tanks, gunfire and regular explosions are audible Friday across Kyiv as the fighting's moved inside the city after Russia entered its outskirts, according to the Ukrainian defense ministry. 

Ukraine is arming civilians with no age limit as Russia moves deeper into its territory, and bloody urban insurgency is possible as Ukraine's formal military falls to Russia's much stronger forces. Ukraine's given out approximately 18,000 automatic rifles to citizens in the past day. 

Zelenskyy said Thursday Russian sabotage groups have entered Kyiv and are after him and his family. 

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"According to our information, the enemy marked me as the number one target. My family is the number two target," Zelenskyy said in a social media video. 

Russia's attacks on Ukraine have largely been against its formal military forces, but civilians are also being killed. 

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Biden has sent troops into NATO countries bordering Ukraine and announced Thursday that the U.S. will send 7,000 more troops to Germany as a further deterrence against additional Russian aggression in the area. 

Many geopolitical experts are warning that Putin's ambitions may not end in Ukraine and he could be interested in conquering other post-Soviet states, including the Baltics. Putin previously said he believes the fall of the Soviet Union was the greatest geopolitical tragedy of the 20th century. Biden warned about those ambitions Thursday. 

"He has much larger ambitions in Ukraine.  He wants to, in fact, reestablish the former Soviet Union. That’s what this is about," Biden said. "And I think that his — his ambitions are — are completely contrary to the place where the rest of the world has arrived."

Fox News' Nana Sajaia and Steve Harrigan contributed to this report.