One goal of the president's trip, McMaster said, will be "to develop a common approach to Russian Federation".
"A leak on what we've been exactly discussing, by the way, happened again on the American side", Lavrov said.
Trump will also meet with other world leaders, national security adviser H.R. McMaster said.
Trump's National Security Adviser H.R. McMaster said Putin would be among the "many world leaders" meeting the USA president during the summit, taking place on July 7 and 8.
Contacts between Russia and the United States are under intense scrutiny following allegations by US intelligence officials of Russian interference in last year's USA presidential election.
In the midst of the 2016 election, self-described whistleblowing organisation Wikileaks uploaded a tranche of emails that were stolen from the account of Clinton's campaign manager John Podesta, including many that embarrassed the then-frontrunner.
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The record for migrants rescued on a single day stands at 7,000, plucked from their unseaworthy vessels on 29 August 2016. German Chancellor Angela Merkel said Thursday that "we will help Italy" with the asylum-seeker crisis.
A top aide to Russian President Vladimir Putin has said the lack of progress in mending ties between Russia and the USA is damaging not only for the two countries themselves but also for the wider global community.
The top Democrat on the House intelligence committee said that if President Donald Trump doesn't act on the threat Russian Federation poses, he could be derelict in his duty to protect the United States.
Some advisers recommended that the president instead do either a quick, informal "pull-aside" on the sidelines of the summit, or that the USA and Russian delegations hold "strategic stability talks", which typically don't involve the presidents.
Russian officials, speaking on condition of anonymity, say they are frustrated that the Trump administration has not been able to engage effectively with Russia on important issues. He said Secretary of State Rex Tillerson, who visited Moscow in April and met with Putin, has played a leading role in the bilateral relationship.
Such concessions could include returning two diplomatic compounds in the U.S. to Russian Federation or lessening sanctions.
A proposed new package of sanctions on Russian Federation in the U.S. Congress might complicate Trump's desire for warmer relations with Moscow.