Mr Trump has drawn strong criticism from both Republicans and Democrats over his initial reluctance to blame Russian Federation for alleged meddling in the 2016 United States elections that he won. But if he acknowledges Russia's involvement in that election, he would be undermining the legitimacy of his own election.
Since Monday's summit and joint news conference in Helsinki, Trump and his aides have been trying to control the damage done when he stunned the world by siding with Putin over US intelligence agencies on the question of Moscow's meddling in the 2016 USA election.
But Mr. Trump added, "Now, with that being said, if that doesn't work out, I'll be the worst enemy he's ever had". Russia's Foreign Ministry said the call was initiated by the American side. If that meeting takes place in Washington, I think it is all to the good.
She cited comments from the current director of national intelligence, Dan Coats, confirming that the threat remains ever-present.
"The Russian effort to influence the 2016 presidential campaign is just one tree in a growing forest", he said.
"Who do you believe?", Lemire had asked, referring to Trump's well established disbelief in the USA intelligence community's ironclad conclusions about Russia's efforts to subvert America's democracy.
Clinton questioned why Trump did not confront Putin over Russia's election interference.
"The sentence should have been: 'I don't see any reason why it wouldn't be Russian Federation, '" he said. The Kremlin had said in April that the president had invited the Russian leader to the White House when they spoke by telephone in March.
The language used by Democrats was harsher.
Russia's ambassador to the U.S., Anatoly Antonov, said the two leaders had discussed the possibility of a referendum in separatist-leaning eastern Ukraine during their Helsinki summit. Other speakers included NY gubernatorial candidate Cynthia Nixon and activist Rose McGowan. Trump was initially warm to the proposal, proposed by Vladimir Putin, calling it "an incredible offer".
His position on Putin and Russian Federation will undoubtedly be an issue in the campaign.
"The Summit with Russian Federation was a great success, except with the real enemy of the people, the Fake News Media", he tweeted. "And to come out against him, as I believe she has recommended, would be totally inappropriate and totally wrong and I couldn't disagree more".
"He wants to undo the architecture of the post-world war two world", she insisted.
He told confidants in the days that followed that he was pleased with how his summit with Putin went, believing he had taken the measure of the man and opened the door to deals down the road on a number of thorny issues.
Removal of U.S. forces on the ground, now about 2,200, is seen as reducing whatever leverage the United States has to press both Russian Federation and Iran.