Washington (CNN) Congressional lawmakers still know very little about what was said during last month's one-on-one meeting between President Donald Trump and Russian leader Vladimir Putin, a point members of the Senate Foreign Relations Committee made very clear Tuesday during a hearing on US relations with Moscow.

In his opening remarks, the committee's Republican chairman, Sen. Bob Corker, told witnesses from the State and Treasury departments that the Trump administration has provided few details about the meeting in Helsinki despite repeated requests from Congress.

"We'd like to understand what was agreed to when the leaders of our two countries sat down in Helsinki," Corker said.

"Were there discussions regarding current or future arms control agreements? What other promises or assurances were made? To date we have received no real readout, even in a classified setting, of this meeting," he added.

The ranking Democrat on the committee, Sen. Bob Menendez, also expressed his frustration over the administration's "lack of transparency" regarding the Helsinki summit saying lawmakers remain "in the dark as to what the two leaders discussed."

"We continue to hear more information -- accurate or not -- from the Russian government than from our own," Menendez said. "This is not only embarrassing, but I believe this lack of transparency has implications for our national security."

"I am not convinced that those who need to know in our own executive branch have a full understanding of what happened," he added.

Demanding details

Pompeo clashed with both Republicans and Democrats on several occasions when he appeared before the Senate committee last month, refusing to provide substantive details about the Trump-Putin sitdown, as well as Trump's meeting with North Korean leader Kim Jong Un in Singapore.

"We've been asking Secretary Pompeo to come and explain the Trump administration's strategy on North Korea and Russia for a long time and they have failed to provide the necessary briefings or hearings to either the full Senate or the Foreign Relations Committee," Menendez said in a statement to CNN.

"After three hours of testimony from the secretary last month, we still have no clarity on the policies our government is pursuing," he added. "On each of the matters, we expect the Trump administration to brief the full Senate as has been done by previous administrations, and to come before the national security committees in open hearing in front of the American people."

Rather than divulge specifics of that conversation, Pompeo highlighted several policy measures he said indicated the Trump administration is committed to being tough on Russia but also open to dialogue -- a stance that was echoed again on Tuesday by A. Wess Mitchell, the State Department's assistant secretary for the Bureau of European and Eurasian Affairs.

When pressed for specifics by Massachusetts Democrat Sen. Ed Markey, Mitchell said that discussions between Trump and Putin were "not deeply substantive."

"The only agreement that came out of Helsinki was for the two national security counsels to meet again, which they are doing this week," Mitchell said, later adding that he has "received the information I need to do my job as it relates to Russia."

National security adviser John Bolton is due to meet this week in Geneva with top Russian counterparts. He said on Sunday, before the latest allegations of Russian interference emerged, that he would raise the issue of election meddling.

"Does that mean that you have been briefed on the INF Treaty? Did the President say to Putin that Russia is in violation a treaty that deals with nuclear weapons threat to the United States?" Markey asked, again probing for details.

"I am not aware of any part of the conversations that was devoted to the subject of INF," Mitchell responded referring to the Intermediate-Range Nuclear Forces treaty, an arms control agreement between Moscow and Washington that has been in force for 30 years.

The latest round of bipartisan criticism related to the Helsinki summit comes as Trump is facing fresh political heat over his relationship with Putin stemming from details of a new Russian hacking strike against the US.

Claims that Russian hackers targeted conservative think tanks critical of Trump and the US Senate emerged hours after the President again cast doubt on Moscow's interference in the 2016 presidential race in an interview with Reuters -- again exposing the odd divide between the President and his own national security and intelligence establishment on the issue.

Rand Paul talks 'carrots'

Republican Sen. Rand Paul used his time during Tuesday's hearing to once again raise concerns about the effect US sanctions on Russia may be having on the prospect of better relations with Moscow.

"I think there are arguments to be made that perhaps more sanctions aren't the way to go. Sanctions are sort of the stick, and the question is, what is the carrot?" Paul said.

"I would say that one of the carrots might be considering whether or not we continue to insist that Ukraine and Georgia be in NATO," he added, arguing that "an agreement not to have Ukraine and Georgia in NATO might lead to less conflict in both Ukraine and Georgia."

Earlier this month, Paul said that he plans to ask Trump to lift sanctions on members of the Russian legislature so that they are able to travel to the United States for meetings with US officials.

The Kentucky senator invited the Russian lawmakers to the US capital during a trip to Moscow in early August and previously told Fox News that members of both houses of the Russian Federal Assembly have "agreed to come to Washington in the fall for further meetings."

"The downside is the chairman of each of the committees is banned from coming to the United States because of sanctions," Paul said on Fox News earlier this month. "So one of the things I'm going to ask the President -- I'm going to talk to the President this weekend -- is I'm going to say, 'why don't we take people off the list who are in the legislature?'"