Trump said the two leaders agreed at the end of Thursday's call that their high-level advisers would meet next week, but he did not give an exact date for their meeting in the Hungarian capital. Putin and Trump last met in Alaska in August.

Peskov said today that their meeting should take place as soon as possible, but that several issues still need to be resolved before that happens, including who will be in the negotiating teams of the two leaders, reports the German news agency dpa.

He added that Russian Foreign Minister Sergei Lavrov and US Secretary of State Marco Rubio will speak by phone before the meeting and begin work on determining the teams. According to Peskov, the meeting between Putin and Trump could take place in the next two weeks or a little later.

Putin spoke today with Hungarian Prime Minister Viktor Orban, who offered to host the summit, and Putin accepted the proposal, according to the French news agency AFP. Orban said after the conversation that preparations for the meeting were in full swing.

Russia is said to have demanded security guarantees for Putin's participation ahead of the leaders' meeting, as the Russian leader is still subject to an arrest warrant issued by the International Criminal Court (ICC), which accuses him of being responsible for the abduction and deportation of children and minors from Russian-occupied Ukrainian territories to Russia.

Hungary announced its withdrawal from the ICC in April, and parliament approved the decision in May. But the withdrawal will not take effect until a year later, meaning Hungary is still legally obligated to arrest Putin if he enters the country.

Hungarian Foreign Minister Peter Szijjarto said today that Hungary will ensure Putin's entry into the country so that he can conduct successful negotiations.

"We await President Vladimir Putin with joy and respect, and of course we will ensure that he can enter Hungary, conduct successful negotiations here, and then return home," Szijjarto explained at a press conference.