Media outlets objected this week when the White House barred a CNN reporter from attending a press event with President Donald Trump because she had earlier called out questions Trump didn't like at an Oval Office meeting.
Putin said Friday he is ready to invite Trump if conditions are right, and he is also ready to visit Washington.
Earlier, the White House said Trump would postpone his invitation for Putin to visit until next year because it believed Mueller's "witch hunt" would be over by then.
"Sounds to me like someone is trying to make up stories in order to get himself out of an unrelated jam", Mr. Trump said.
"I understand perfectly that President Trump has a desire to hold further meetings, and I am ready to come to Washington if appropriate conditions for work are created".
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The White House has taken steps in recent days to tamp down on the concerns over the United States' Russia policy sparked by the Helsinki summit, where Trump appeared to side with Putin and cast doubt on the US intelligence community's conclusion that Russia interfered in the 2016 presidential election.
The Kremlin chief spoke after the United States administration earlier this week delayed a second summit between Putin and Trump to next year under fire from critics at home.
"President Trump looks forward to having President Putin to Washington after the first of the year, and he is open to visiting Moscow upon receiving a formal invitation", White House press secretary Sarah Sanders said in a statement.
Putin added that Russian Federation and the United States also have plans for contacts at G20 summits and other worldwide gatherings.
US President Donald Trump waves next to First Lady Melania Trump (L) as they board Air Force One at Andrews Air Force Base in Maryland on July 27, 2018.
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Actuellement en vacances avec sa copine Pamela Anderson , Adil Rami arrive quand même à faire parler de lui . Et même si le community manager a rapidement supprimé son tweet, il n'aura pas échappe à Adil Rami .
The White House complained about questions she shouted to Trump earlier about Russian Federation and Michael Cohen.
Both Trump and Putin have said they are determined to improve relations.
However, efforts to achieve a detente have been fiercely resisted by the USA lawmakers, including some in Trump's own Republican Party, who accuse him of being too friendly towards Putin.
The pair met last week for closed-door talks in Helsinki. "We need to minimise risks, we see what's happening with sanctions. There are some things you can't do over the phone". I think it's something that North Atlantic Treaty Organisation has to look at.
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For about half the world, the " blood moon " will be partly or fully in Earth's shadow from 1:14 p.m.to 7:28 p.m. The eclipse will have been visible from Africa to the Middle East, Europe, Russia, India, and Australia.