WASHINGTON - US President Donald Trump said on Sunday that he discussed with Russian President Vladimir Putin forming a cyber security unit in their first meeting amid speculation about his acceptance of Putin's denial of Russian meddling in the US election.

"Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded and safe," Trump tweeted on Sunday.

"...Now it is time to move forward in working constructively with Russia!" Trump wrote on another tweet.

The first face-to-face encounter between Trump and Putin came on Friday on the sidelines of the G20 summit in Hamburg, Germany.

After the meeting, Russian Foreign Minister Sergey Lavrov told reporters on Friday that Trump had accepted Putin's denial of Russian meddling in the US election.

Putin himself also said on Saturday that he left the meeting with the impression that Trump had accepted his denial.

"He asked questions, I replied. It seemed to me that he was satisfied with the answers," Putin told reporters on Saturday.

During his visit to Ukraine on Sunday, US Secretary of State Rex Tillerson, the only other US official in the Trump-Putin meeting, did not answer directly when asked whether Trump had accepted Putin's denial.

On another tweeter on Sunday, Trump said that he "strongly pressed President Putin twice about Russian meddling in our election."

"...He vehemently denied it. I've already given my opinion..." Trump said.

The idea of forming a cyber security unit with Russia was soon met with criticism within Trump's own Republican Party.

Speaking at a TV interview aired on Sunday, Republican Senator Lindsey Graham called the idea "pretty close" to the dumbest idea he'd ever heard.

"He (Trump) is literally the only person I know of who doesn't believe Russia attacked our election in 2016," said Graham.

"This whole idea about moving forward without punishing Russia is undermining his entire presidency," he added.