Trump also said he misspoke in Helsinki.
Even New Hampshire's new GOP chairman, Wayne McDonald, took a swipe at Horn for attacking Trump on Russian Federation.
Mr Trump's decision to invite Mr Putin to Washington has been criticised as Moscow is accused of meddling in the 2016 U.S. presidential election campaign.
The invitation came after Mr Trump's first summit with Mr Putin in Finland.
In an interview with CBS Evening News, which was released in part on Wednesday evening, Trump was asked whether he holds Putin personally responsible for the meddling in 2016. Once he got there, he returned to Twitter to complain about news coverage of Monday's meeting.
The president claimed he'd misspoke during his summit with Putin and agreed with the USA intelligence community that Russian Federation had interfered in the election, though he added it could be "other people also". "In the Old Days they would call it Diplomacy".
"If I was loud and vicious, I would have been criticised for being too tough".
GOP officials from across the country said they were willing to give Trump the benefit of the doubt, believing that he probably was much firmer with Putin in private than he was in his public performance.
And Sanders created a fresh headache for the administration when she said the White House was still reviewing a proposal from Putin to allow access by Russian law enforcement officials to Americans whom the Kremlin accuses of unspecified crimes in return for US access to interrogations of Russian agents indicted for their alleged roles in interfering in the 2016 election. The timing of that announcement was "unfortunate", said the official who defended Coats.
Theresa May: EU must change ‘unworkable’ Brexit position
During her visit, the prime minister is also due to speak to young people in Belfast about Northern Ireland's future. If "no deal" produces a hard border, it will not be better than a "bad deal" for people living here.
One stop Putin nearly surely won't make is Capitol Hill.
"You particularly need a note taker so that there can be no mistake about what was said", she said.
The president was asked what he said to Putin, and he replied that he was "very strong on the fact that we can't have meddling". Trump may like doing things his way, eschewing advice and precedent like no president before, but he never likes being alone. "Those conversations are incredibly important". Last November, 53 percent said USA leadership had grown weaker; it's in fact slightly lower now.
A White House meeting would be a dramatic extension of legitimacy to the Russian leader, who has always been isolated by the West for activities in Ukraine, Syria and beyond and is believed to have interfered in the 2016 presidential election that sent Trump to the presidency. "Meanwhile, we're hearing crickets from the White House". The highly choreographed affairs had been sought out by the USA leader as a way to boost his credibility overseas and his favorability at home, and he believed the latest one had accomplished the task.
Asked about hosting a Summer Olympics in Russian Federation for the first time since 1980, Putin says feasibility studies need to be conducted "but obviously we will organize major worldwide competitions here", in comments reported by state news agency RIA Novosti.
It wasn't until more than 24 hours after the press conference that Trump took back his initial remarks, blaming a grammatical glitch as he read from a prepared statement: "The sentence should have been: I don't see any reason why it wouldn't be Russian Federation". He did not elaborate on what Putin's solutions would be.
"The added funds will provide equipment to support ongoing training programs and operational needs, including capabilities to enhance Ukraine's command and control, situational awareness systems, secure communications, military mobility, night vision, and military medical treatment", the Pentagon said in a statement.
On Tuesday, Russia suggested there had been more than one agreement forged by two leaders and even said it was ready to implement agreements reached by Mr. Trump and Putin.
"Russia should suffer consequences for its aggressive and destabilizing behavior as well as its continuing illegal occupation of Ukraine", Mattis said in a letter to Senate Armed Services Committee Chairman John McCain.
At a festival appearance in New York City's Central Park, Hillary Clinton spoke against President Trump's apparent reluctance to accept intelligence showing that Russian Federation interfered in the 2016 presidential election. She said Trump was saying "no" to answering additional questions - although that didn't appear to be the case because he elaborated on Russian Federation.