MOSCOW (Reuters) - Russian and U.S. teams plan to meet this week to discuss improving relations after the war in Ukraine had pushed ties to the worst level since the depths of the Cold War, a senior Russian start diplomat said on Sunday.

With Russian forces having advanced last year at the fastest rate in Ukraine since the start of the 2022 invasion, U.S. President Donald Trump has said he wants to deliver a peace deal to end the war which he says has killed vast numbers of people.

Trump and President Vladimir Putin spoke on February 12 about improving relations and ending the war, and U.S. and Russian officials met in Riyadh on February 18 to that end.

Russian Deputy Foreign Minister Sergei Ryabkov, Moscow's point man for relations with the U.S., said that a meeting at the level of departmental heads would take place at the end of the week.

"We are open to contacts with the American side, in particular, on irritants in bilateral relations," Ryabkov was quoted as saying by state news agency TASS.

"We are waiting for real progress when the meeting scheduled for the end of the coming week takes place."

Trump has repeatedly said that he believes Putin and Ukrainian President Volodymyr Zelenskiy want to do a deal.

Trump said on February 12 that it was not practical for Ukraine to get NATO alliance membership and that he had seen support for U.S. Defense Secretary Pete Hegseth's statement that Ukraine will not realistically return to its 2014 borders.

As the war enters its fourth year, Russia controls nearly one fifth of Ukraine - or an area about the size of the U.S. state of Ohio - including Crimea which Russia annexed in 2014, about 75% of the Donetsk, Zaporizhzhia and Kherson regions and more than 99% of the Luhansk region.

Russia says the land it controls is now Russian land under Russian law and the Russian nuclear umbrella, a position Ukraine and its Western European backers have said they will never recognise or accept.

Last June, Putin set out his terms for an end to the war: Ukraine must officially drop its NATO ambitions and withdraw troops from the entirety of the territory of the four Ukrainian regions claimed and mostly controlled by Russia.

(Reporting by Reuters; editing by Guy Faulconbridge)