Ukrainian President Volodymyr Zelenskyy says he will visit the US next month and present President Joe Biden with a plan to end Russia's invasion.

Zelenskyy spoke about the plan at a news conference in Kyiv on Tuesday.

He told reporters that Ukraine's cross-border offensive in the western Russian region of Kursk is part of the plan. Ukraine launched the incursion in early August.

Zelenskyy said the plan also includes his country's strategic place in the world's security infrastructure and a package to put diplomatic pressure on Russia.

He went on to say that in September he will meet Biden and also convey the plan to US Vice President Kamala Harris and former President Donald Trump, the two major-party presidential nominees.

Zelenskyy stressed the main point of the plan is to force Russia to end the war, and that he wants to end it on fair terms for Ukraine.

Zelenskyy also said Ukraine has successfully tested its first domestic ballistic missile. He added Western-supplied F-16 fighter jets are already in operation and were used to destroy Russian missiles.

The Ukrainian military Commander-in-Chief Oleksandr Syrskyi said his forces have taken control of 1,294 square kilometers of land, which includes 100 settlements, during their operation in Kursk. He also said 594 Russian soldiers have been taken prisoner.

The military chief added the situation is "fairly difficult" on the Pokrovsk front in eastern Ukraine. He said Russian forces are using their advantage in personnel, weapons and military equipment, and are actively using artillery and aviation.