The United States has proposed its own UN resolution on the war in Ukraine, competing with a European-backed statement demanding the withdrawal of Russian forces.

The UN General Assembly will have a special session on Monday, as it marks the third anniversary of Russia's invasion of Ukraine.

The draft resolution from the European Union and Ukraine refers to "the full-scale invasion of Ukraine by the Russian Federation" and demands that Russia "immediately, completely and unconditionally withdraw all of its military forces from the territory of Ukraine."

By contrast, the US submitted its own resolution on Friday imploring "a swift end to the conflict" without using words critical of Moscow, such as "invasion."

US Secretary of State Marco Rubio said in a statement that the resolution is consistent with President Donald Trump's view. He urged all UN member states to join the US.

Meanwhile, Russia's state-run media reported a remark by Russian Deputy Foreign Minister Sergey Ryabkov on Saturday that top officials from the US and Russia will have the second round of talks within two weeks with the aim of ending the war.

The report says the talks will take place in a third country but the location has not been determined.