After aides leaked embarrassing details of Trump's shock decision to call Putin and congratulate him on re-election, the United States president blamed the media for the furor and insisted Moscow can be a solid partner.
Trump's move to congratulate Putin for securing a fourth term in power drew swift criticism for breaking a taboo among western leaders.
It comes as Trump and White House officials are said to be fuming over a leak of Trump's briefing materials for the Tuesday call, in which aides warned Trump against congratulating Putin.
In addition, the two presidents expressed satisfaction with the apparent easing of tensions over North Korea's weapons program, according to the Kremlin.
"We don't get to dictate how other countries operate". Since then, his administration has quietly taken some steps to curb Moscow's influence, approving new arms sales to Ukraine and issuing sanctions against Russians involved in the aforementioned meddling.
The leakiness of this White House is nothing new. Though the reaction has been described as "rattled", a White House official said it is more like anger and disappointment.
Nor did they address Washington's imposition last week of a new round of sanctions against Moscow created to punish Russians responsible for attempts to interfere in the 2016 U.S. presidential election.More news: Fifth package bomb explodes in Texas at FedEx facility in San Antonio
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Johnson said applications to go to Russian Federation for the World Cup were about a quarter of what they were at this stage ahead of the 2014 World Cup in Brazil.
"The two leaders confirmed the need for the United States and Russian Federation to continue our shared efforts on strategic stability", it said.
Trump's overture to Putin was criticized by top senators in his own Republican party, who called Sunday's election a sham.
Republicans in Washington were critical of Trump's decision to congratulate Putin, but also lined up behind the president in anger about the leak.
The White House had earlier indicated that no call with Putin was planned, as the Russian leader played down talk of a rift.
Johnson also said the timing of an attack using military-grade nerve agent against a former Russian spy in England was probably connected to the weekend election won by Putin.
Putin said Monday he would address disputes with the West but stressed that worldwide relations were a two-way street.