"As the president has made clear, he would like the United States and the leaders of the entire West to develop a more constructive relationship with Russian Federation", said Trump's top security adviser.
There has been speculation that the two would meet at the event, but it wasn't solidified until McMaster's confirmation Thursday.
Trump has long played down reports of Russian meddling, but he seized on recent reports about former president Barack Obama's cautious reaction to election interference previous year to attack Obama for a timorous response.More news: Fabulous Federer trounces Zverev to claim ninth Halle title
The president raised eyebrows for heaping praise on Putin during the campaign, but denied having a "relationship" with the Russian leader.
Trump wants a full diplomatic session with his Russian counterpart, including media access and the typical protocol associated with such meetings, when the two attend the G20 summit next month in Germany, but officials within the State Department and the National Security Council are urging restraint, according to the Associated Press.
Trump has struck a tough tone on Russia's ally Syria, ordering a missile attack on a military base there in April after it reportedly was used to launch a chemical attack; and warning this week that the government of Bashar al-Assad would "pay a heavy price" if it carried out a new chemical attack. The United States backs rebel groups trying to overthrow Assad, and Washington angered Russian Federation by launching missile strikes against a Syrian government air base in April.
They say the issue is not Trump himself, but the stand-off inside the US political system which, they say, means the USA president is liable to be attacked by domestic opponents if he makes any overtures towards Russian Federation.More news: China's FM Meets Pakistan's Aziz, Discusses Peace In Afghanistan
"They will meet" on the sidelines of the G20, Mr Putin spokesman Dmitry Peskov said, but added that "no preparations" are being made for any separate meeting at the moment.
In the last days of his presidency, Obama ordered the expulsion of 35 Russian suspected spies and imposed sanctions on two Russian intelligence agencies over their involvement in hacking us political groups in the 2016 election.
Lavrov said U.S. Secretary of State Rex Tillerson called him and informed him of the alleged Syrian government plot to use chemical weapons, but Lavrov said he urged the U.S. against using the allegations as a "pretext" for war.
"Our relationship is at an all-time low, and it's been deteriorating further".More news: Eid Al Fitr to be celebrated tomorrow
The U.S. Senate reached an agreement on Thursday to resolve a technical issue stalling the sanctions, although the measure's fate in the House of Representatives is uncertain.