Russian president Vladimir Putin earlier met Mr Trump's national security adviser for talks meant to set the stage for the US-Russian summit. He spoke of a possible joint declaration on improving U.S. -Russia relations and worldwide security. For more on this, RT's America Manila Chan joined by former Pentagon official Michael Maloof.
The TASS news agency reported that Bolton had discussed potential cooperation between the two countries' security councils with Yuri Averyanov, the first deputy secretary of Russia's Security Council. The Kremlin would not say whether Bolton would also meet with President Vladimir Putin.
Putin also sent his regards to Trump via Bolton, and said "he attaches great importance to the upcoming meeting", according to the statements by the Kremlin and Ushakov.
Asked in a conference call with reporters about specifics for the meeting, Peskov said, "Let's wait for the actual meeting to happen, when Putin receives Bolton".
The venue and date for the Trump-Putin summit were to be formally announced Thursday by both sides, Bolton said earlier in Moscow.
"A very convenient place for us and the American side has been selected in a third country", he added.
As for "the meaning of [this meeting] with respect to. anyone else that you mentioned, I think I'll just duck the question", Bolton added.
U.S. - Russian relations have been strained for years over disagreements about Syria, Russia's actions in Ukraine and its annexation of Crimea.
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Despite worldwide sanctions against Moscow for its actions in Ukraine, Syria, and elsewhere, Bolton noted that world leaders have continued to meet with Putin.
As he greeted John Bolton in the Kremlin, Mr Putin noted that US-Russian relations are at a low point, which he said was mostly due to US political infighting.
"I think the fact of the summit itself is a deliverable", he said. However, an array of new Russian sanctions has been imposed under his presidency. Subsequent sanctions have punished Moscow for what Washington has called its malign behavior and meddling in US politics, something Russian Federation denies.
Vienna, Austria is seen as a possible location for that meeting. But planning for the meeting was delayed amid the investigations into whether Trump's campaign colluded with Russian Federation. Subsequent sanctions have punished Moscow for what Washington has called its malign behavior and alleged meddling in US politics.
Bolton said he did not necessarily expect the summit to produce specific outcomes.
Trump's trip includes a North Atlantic Treaty Organisation conference in Brussels, and the American president is at odds with allies over their levels of defense spending as well as policy toward Russian Federation.
This intimate approach of both leaders will be the ideal scenario for Putin to demonstrate his political superiority over his historic enemy, ending the United States' "unilateral domination" over world affairs.