Trump 'absolutely did not believe' Putin's denial of election meddling, official says White House chief of staff pushed back on Russia's narrative on Trump meeting.

 -- President Trump’s chief of staff pushed back against a narrative by Russia that Trump accepted Russian President Vladmir Putin’s denial of having interfered in the U.S. presidential election.

“The president absolutely did not believe the denial of President Putin," White House chief of staff Reince Priebus said on “Fox News Sunday” of Trump's meeting with Putin on Saturday.

Priebus’ assertion came on the same morning that Trump tweeted that it is time to work "constructively with Russia."

Priebus said the president's call to deal constructively with Russia doesn't mean the election interference is being ignored.

"It doesn't mean they're off the hook," the chief of staff said. "What it means is we're not going to forego progress simply because we have a disagreement in regard to this meddling in the United States election."

"What it means that we have to move forward with things like a cease-fire in Syria ... move forward with ISIS ... and resolving the conflict in Ukraine," Priebus said.

Trump in his Sunday morning tweetstorm also returned to frequent topics of his in regard to Russia's election interference. He accused former President Obama of not acting in response to the alleged hacking and raised questions about both the media's reporting on the revelations of the election interference and the Democratic National Committee's response.

The president also said the possibility of the U.S. lifting its sanctions against Russia didn't come up in his meeting with Putin.

Trump's tweets and Priebus' remarks came after Putin said at a press conference Saturday that he believes the U.S. president was "satisfied" with his answers to questions about Russia's alleged interference in the 2016 U.S. presidential election.

The Russian leader said Trump brought up the alleged election meddling and asked "many questions" about the topic.

"I answered all these questions as much as I could. It seems to me that he took note of this and agreed," Putin said in his native tongue at the televised press conference, which was translated by Russian news agency Interfax.

"He really was interested in some details. I, as far as I could, answered all this in detail," Putin added, when pressed further by reporters about the meeting with Trump. "He asked me, I answered. He asked clarifying questions, I explained. He appeared to me satisfied with these answers."

Putin said he reiterated to the U.S. president that there was no basis for such allegations.

"Our position is well-known," Putin told reporters. "There is no ground to believe that Russia interfered in the U.S. electoral process."

Prior to Putin's press conference Saturday, Russian Foreign Minister Sergey Lavrov told the media Friday that Trump raised the issue of election meddling. He said the U.S. president accepted Putin’s “clear statements” that “Russian leadership hadn’t interfered.”

A senior White House official, when asked by ABC News whether Lavrov's description of Trump’s accepting Putin's denial of election interference was true, said, “No,” without providing further information.

During an off-camera briefing Friday, U.S. Secretary of State Rex Tillerson told reporters that the alleged election interference was the first subject Trump raised at the meeting with the Russian leader.

"The president opened the meeting by raising the concerns of the American people regarding Russian interference in 2016 election. Putin denied such involvement, as he has done in the past," Tillerson said. "The two leaders agreed this is of substantial hindrance. They agreed to exchange further work regarding commitments of noninterference in the affairs of the U.S. and our democratic process as well as other countries.”