He also said Moscow is ready to discuss a possible visit by Putin to Washington after a surprise invitation from Trump.
Huckabee Sanders also announced that the White House would not proceed with a plan to extradite U.S. citizens to Russian Federation for questioning in exchange for Russian Federation allowing its intelligence officials to be questioned as part of the Mueller probe.
He said he hadn't seen Trump's invitation himself, but that "Russia was always open to such proposals".
"The warning signs are there", he said.
"I think as time goes by and the president has already mentioned some things that happened in that meeting, I think we will learn more".
Trump himself tweeted: "The Summit with Russian Federation was a great success, except with the real enemy of the people, the Fake News Media".
Republican and Democratic U.S. lawmakers grappled with Trump's conflicting statements about the summit and what they did not know: exactly what the two leaders discussed and what agreements, if any, were reached.
Following his summit with Vladimir Putin, President Trump has been fighting accusations he failed to stand up to the Russian leader.
It comes after Mr Putin, asked in Helsinki whether he would extradite the 12 Russian intelligence agents indicted in the U.S. for hacking Democratic Party computers, said he would meet the USA government "halfway".
"This issue (of a referendum) was discussed", he said, adding without elaborating that Putin made "concrete proposals" to Trump on solutions for the four-year Ukraine conflict, which has killed more than 10,000 people.
The photo illustration "is meant to represent this particular moment in USA foreign policy, following the pair's recent meeting in Helsinki, Finland", CNN quoted Time as saying in a recently released statement.
Critics complained that instead of taking a firm stand against Vladimir Putin over Russian interference in the USA election, Donald Trump accepted his denials over the word of American intelligence agencies. This came mere seconds after Putin admitted in a press conference that he had be hoping for him to win over rival Hillary Clinton. The sign seemed to read "Nuclear Weapon Ban Treaty". A day earlier she didn't shoot down the idea, instead saying Trump was "going to meet with his team" about it. He abruptly changed the subject to Hillary Clinton. "That's the action of a majority that's burying its head in the sand and acting to protect the president rather than to protect the public interest". "Can you name a single fact?" he asked.
Senate Republicans joined Democrats in swiftly passing a resolution, 98-0, that put the Senate on record against the questioning of American officials by a foreign government.
"Obviously I wished he had made a different statement", he said.