A delegation of senators looked to up pressure on Russian President Vladimir Putin Saturday, as tensions around Ukraine heightened.

The eight lawmakers blasted the Russian leader while traveling through Ukraine and called Sunday's secession referendum in Crimea rigged and illegitimate. Some of the senators asked for the U.S. to provide military equipment to Ukrainian troops, and the group vowed crippling economic sanctions against Russia until the nation pulled back.

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“This is the person that stated that the greatest catastrophe of the 20th century was the breakup of the Soviet Union,” said Sen. John McCainJohn McCainWebb: What matters now is policy McCain questions Trump budget pick's support for military Why the era of US global leadership is over MORE (R-Ariz.) of Putin. “We have to treat him for what he is. That does not reignite the Cold War, but it means we enact steps that make it clear ... that his ambitions will not be realized by the great community of nations that would resist him.”

“There’s one person I hold accountable for this aggression. It’s Vladimir Putin,” added Sen. Ron JohnsonRon JohnsonLive coverage: Trump budget chief faces two Senate panels Overnight Healthcare: GOP governors defend Medicaid expansion GOP senator: Let's work with Dems to 'fix' ObamaCare MORE (R-Wis.). “If there’s further bloodshed, there’s also one person I will hold accountable.”

The bipartisan group hoped their presence in Ukraine would underline the united support the U.S. is providing to the nation, ushering in a new government while Russian forces are amassing along its border.

“We are standing here united,” said Sen. Chris MurphyChris MurphySenate confirms Trump's UN ambassador GOP, Dems hear different things from Trump Live coverage of Trump's inauguration MORE (D-Conn.). “There will be consequences for the actions that have already been taken ... there’s a price to be paid for this type of aggression.”

The other senators in the delegation were Sens. Dick DurbinDick DurbinJustice requires higher standard than Sessions Warren burns Mnuchin over failure to disclose assets Trump Treasury pick to defend foreclosure record MORE (D-Ill.), Sheldon WhitehouseSheldon WhitehouseFive takeaways from Pruitt's EPA hearing Health pick’s trades put STOCK Act in spotlight Dems prepare to face off with Trump's pick to lead EPA MORE (D-R.I.), John BarrassoJohn BarrassoBooker is taking orders from corporate pharmaceuticals Graham to vote for Trump’s EPA pick Pruitt says his EPA will work with the states MORE (R-Wyo.), John HoevenJohn HoevenCabinet picks boost 2018 Dems Five regulations that could come in Obama's final days ND senator calls for remaining Dakota Access protesters to leave MORE (R-N.D.) and Jeff FlakeJeff FlakeThis week: Congressional Republicans prepare to huddle with Trump GOP eyes new push to break up California court Live coverage of Trump's inauguration MORE (R-Ariz.).

While McCain and Durbin have backed sending weapons to Ukraine, no senator suggested that the U.S get directly involved in a military response.

The group dismissed the legitimacy of Sunday’s election on the future of Crimea, as McCain called it “phony” and Durbin described it as “Soviet-style.”

Their criticism came shortly after Russia vetoed a United Nations resolution condemning the referendum. China abstained from the vote, but all other voting nations backed it.