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 Sidney McCainGOP strategist donates to Alabama Democrat Meghan McCain knocks Bannon: 'Who the hell are you' to criticize Romney? Dems demand Tillerson end State hiring freeze, consult with Congress 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 JohnsonRonald (Ron) Harold JohnsonOvernight Cybersecurity: Panel pushes agencies on dropping Kaspersky software | NC county won't pay ransom to hackers | Lawmakers sound alarm over ISIS 'cyber caliphate' GOP chairman warns of ISIS's ‘cyber caliphate’ Overnight Finance: House approves motion to go to tax conference — with drama | GOP leaders to consider Dec. 30 spending bill | Justices skeptical of ban on sports betting | Mulvaney won't fire official who sued him 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 MurphyChristopher (Chris) Scott MurphyAvalanche of Democratic senators say Franken should resign Senate passes tax overhaul, securing major GOP victory Dem senator compares GOP tax bill to unicorns, Tupac conspiracy theories 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 DurbinRichard (Dick) Joseph DurbinDemocrats turn on Al Franken Minnesota's largest newspaper calls on Franken to resign Democratic senator predicts Franken will resign Thursday MORE (D-Ill.), Sheldon WhitehouseSheldon WhitehouseOvernight Regulation: Net neutrality supporters predict tough court battle | Watchdog to investigate EPA chief's meeting with industry group | Ex-Volkswagen exec gets 7 years for emissions cheating Overnight Energy: Watchdog probes Pruitt speech to mining group | EPA chief promises to let climate scientists present their work | Volkswagen manager gets 7 years for emissions cheating EPA head pledges to protect climate scientists MORE (D-R.I.), John BarrassoJohn Anthony BarrassoScalise: House, Senate ‘pretty close’ on tax bill Top GOP senator: House and Senate 'not that far apart' on tax bill Sunday shows preview: Republicans take victory lap on taxes MORE (R-Wyo.), John HoevenJohn Henry HoevenMcConnell works to salvage tax bill GOP to reduce tax relief by 0B to win over deficit hawks  The Hill's Whip List: Where Republicans stand on Senate tax bill MORE (R-N.D.) and Jeff FlakeJeffrey (Jeff) Lane FlakeGOP strategist donates to Alabama Democrat Sasse: RNC help for Roy Moore 'doesn't make any sense' Sasse calls RNC decision to resume support for Moore 'bad' and 'sad' 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.