(CNN) -- The United States upped pressure on Moscow over the Malaysia Airlines disaster as Secretary of State John Kerry drew a clearer line to Russia over its ties to rebels in Ukraine and the rocket system used to down the jet. He also noted on CNN that it was a "moment of truth" for Vladimir Putin.
Kerry and key congressional lawmakers from both parties especially sharpened the focus on Putin to, as Senate Intelligence Committee Chairman Dianne Feinstein said, "man up" and lead.
There was concern, however, that Russia's behavior since Thursday's destruction of Flight 17 by a missile the United States believes was fired by the Russian-backed rebels further underscores Putin's hardening preference for Cold War-era politics.
"This is going back to the days of Stalin, and Khrushchev and Brezhnev," Republican Rep. Peter King said on CBS's "Face the Nation."
"The way he's responding to a crisis, which he caused, which everyone knows he did, and yet he goes underground. This is what a mafia guy does. This is what a goon does. Not a world leader. Not someone in the civilized world."
Asked on CNN's "State of the Union" whether the incident has pushed U.S.-Russian relations back to Cold War-era levels, Feinstein simply said, "yes."
Governments from around the world have expressed outrage at the disorderly situation at the remote crash site about 40 miles from Russia's border and called on Putin to use his influence on the pro-Russian rebels to open up the area to investigators and stand aside.
Since the crash that killed nearly 300 people, the Ukrainian government and the rebels have traded bitter accusations over who was responsible and what has been done since.
Russia has denied any involvement, and Putin said Ukraine's military campaign against the rebels was to blame for blowing the Boeing 777 out of the sky.
But Kerry said it would be "ridiculous" for the international community trust what Putin has said.
Kerry said there was a "buildup of extraordinary circumstantial evidence" that the rebels were behind it and that the suspect rocket system used was transferred to them from Russia, which denies its military equipment crossed the border.
"We know with confidence, with confidence, that the Ukrainians did not have such a system anywhere near the vicinity at that point in time, so it obviously points a very clear finger at the separatists," Kerry said on CNN's "State of the Union."
He called a "very, very critical moment for Russia to step up publicly and join in the effort in order to make sure" there is a full investigation.
The crash site near the town of Torez in the Donetsk region is under rebel control and the situation was said to be far from organized.
Negotiations were being held for the release of nearly 200 recovered bodies, and there were reports some of the dead had been looted. International investigators have limited access.
Kerry said that he spoke Saturday with Russian Foreign Minister Sergey Lavrov in what he called a "direct and tough conversation."
Russia needs to help ensure that investigators can conduct a thorough investigation, Kerry said.
"This is the moment of truth for Russia and for Mr. Putin," Kerry said.
Not shooting from hip
But while Kerry urged Russia to allow for a complete investigation, he did not lay out specific repercussions for the Russians. He said they are being discussed with European allies.
He added on "Fox News Sunday" that the United States wasn't going to "shoot from the hip," but instead respond in a "thoughtful way."
When pressed on "Meet the Press" that the Obama administration is giving Russia too much maneuvering room, Kerry said the world is "complicated."
He pointed to Russia's cooperation removing chemical weapons in Syria and other parts of the world.
"Russia is working with us in a cooperative way on the P5 + 1," which are the talks regarding Iran's nuclear program.
The Obama administration criticized
But Senator Lindsey Graham, R-South Carolina, said Kerry's response was not severe enough.
"He didn't call Putin the thug that he is. He didn't call for arming Ukraine so they can defend themselves," Graham said on "Meet the Press."
Reaction from Republicans plays into the ongoing narrative that Republicans paint of the President's foreign policy leadership as being weak and indecisive.
Tennessee Republican Sen. Bob Corker said the response by the Obama administration since Russia began its annexation of Crimea has been "timid and cautious."
It has "kept Putin from really paying a price inside his country for the actions that have been taken," he said on "Fox."
"The United States needs to end its tepid response," Michigan Rep. Mike Rogers, Chairman of the House Intelligence Community, said on ABC's "This Week."
He called for "aggressive" help for the Ukrainian military.
Others called for more even tougher sanctions on Russia's energy and banking sectors, which the administration escalated this past week just before the plane crash.
King, who sits on both the Homeland Security and Intelligence Committees, said global response should also consider relieving Russia from hosting the 2018 of the World Cup.
Pressure on Europeans
Kerry and Republicans and Democrats were in agreement, however, regarding the role of the Europeans who have been reluctant to impose tough sanctions against Russia because of their reliance of Russian energy.
"We hope this will be a wake-up call for some countries in Europe that have wanted to stand back and give this more time and worry about the trade relationship," Kerry said on "Meet the Press," repeating a sentiment expressed by President Barack Obama last week.
Corker said the western countries response to Russia in the past six months has been "tragic."
"I've been indredibly discouraged by not only the U.S. response, but by the European response," he said on Fox.
On the same program, Sen. Bob Menendez, D-New Jersey, chairman of the Senate Foreign Relations Committee, said the United States and Europe have "to have a far more significant response than we've seen to date."
A new Cold War?
Members of Congress issued their own much more dire warning of Putin.
On "State of the Union," Rep. Michael McCaul, chairman of the House Homeland Security Committee, said, "Mr. Putin is returning to a Cold War" posture.
"And I think this is a game changer, what happened, the downing of this commercial flight by separatists tied to Putin," McCaul said.
Zbigniew Brzezinski, former national security adviser for Jimmy Carter, believes Putin, if anything, has started a new Cold War.
"He has gotten himself into horrendous jam. I strongly suspect that a lot of people in Russia, even not far away from him who are worried that Russia's status in the world is dramatically being undermined," Brzezinksi said Sunday on CNN's "Fareed Zakaria GPS."
CNN's Shannon Travis contributed to this report