Sen. Lindsey Graham, R-S.C., is facing rebuke from Republicans in the House and Senate after he touted his effort to pass a bipartisan resolution pushing for Ukraine to be admitted into NATO amid its war with Russia.

Discussing the effort in a tweet, Graham said he believes there's "overwhelming" support for the proposal in the Senate and claimed that Ukrainian membership in NATO is "vital to the future security of Europe and the world."

"I will be working with Republicans and Democrats in the Senate to pass a resolution urging the admission of Ukraine into NATO," Graham said of the effort. "The best way to prevent future wars and promote peace is to create security guarantees that make aggressor nations think twice before starting wars."

"Ukrainian NATO membership is vital to the future security of Europe and the world. I believe there is an overwhelming majority of Senators supporting this proposition," he added.

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Kentucky Republican Sen. Rand Paul shouted down Graham's proposal in a Friday evening tweet, insisting that it is "exactly wrong" and warning that it has the potential to lead the United States into a war with Russia.

"Absolutely not. This is exactly wrong – as usual – and could very well lead us to war with Russia, something no one should want," Paul said in response to a tweet from Graham.

The senator also drew backlash from House Republicans, including Rep. Lauren Boebert, R-Colo., who wrote in a tweet: "I'm sure Lindsey Graham knows this, but this would mean American troops on the ground in Ukraine."

"The American people will not stand by and allow our troops to go die in someone else's war," the congresswoman added.

Taking aim at the proposal and speaking out against it, Rep. Thomas Massie, R-Ky., said that "expanding NATO" does not fall in line with the interests of Americans.

"Expansion of NATO, a Cold War relic, led to the rise of Putin, also a Cold War relic, culminating in the invasion of Ukraine. Expanding NATO further is not in the interests of US citizens," Massie wrote in a tweet.

Echoing Massie, Georgia Republican Rep. Marjorie Taylor Greene spoke out against the proposal and insisted that "America doesn’t support" the senator's proposal.

"This is madness. Everyone in Washington should be urging peace and stopping the war in Ukraine. Not bringing us to the brink of World War 3," Greene wrote in a tweet. "The Ukraine war is destabilizing Europe and changing the world’s economies. America doesn’t support this."

Weighing in on the proposal, Ohio GOP Rep. Warren Davidson claimed that the effort being pushed by Graham is "essentially a declaration of war."

"HARD NO. Russia’s invasion is unjust, but including Ukraine as a member of NATO is essentially a declaration of war," Davidson wrote in response to Graham. "America cannot even agree on a mission statement in Ukraine, and NATO won’t fully fund their own defense. Epically bad idea. Low zero."

Richard Grenell, the former U.S. Ambassador to Germany, also spoke out against the proposal offered by Graham and argued that there should be no new members added to "the U.S. taxpayer's burden" until all members of NATO are paying the "2% spending obligation" they agreed to in 2014.

"[Eight] of the current 31 NATO Members are paying their 2% spending obligation that they made in 2014. No new members should be added to the U.S. taxpayer’s burden until we reach 31/31," Grenell wrote in a tweet.

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Other conservatives were also quick to highlight issues with the South Carolina Republican's proposal, including Mollie Hemingway, a Fox News contributor who serves as editor-in-chief of The Federalist.

"Dangerous rhetoric from warmonger Graham, whose foreign policy track record means you'd be well advised to do the opposite of what he proposes," Hemingway said in a tweet.

Graham's position on the Russia-Ukraine war, which has been ongoing for well over a year, has not been popular among hardcore conservatives.

An ardent supporter of Ukraine's defensive efforts, Graham traveled with Democratic Sen. Richard Blumenthal of Connecticut to Kyiv last summer.

During the meeting on the 134th day of the war, Zelenskyy, according to his office, "called on senators to back the decision on providing Ukraine with modern air defense systems." 

"First of all, we appeal to you so that the Congress supports Ukraine in the matter of supplying modern air defense systems," Zelenskyy said. "We must ensure such a level of sky security that our people are not afraid to live in Ukraine."

President Biden commented this week that he believes now is not the time for Ukraine to join NATO.

"I don't think it's ready for membership in NATO," Biden said in a CNN interview. "I spent, as you know, a great deal of time trying to hold NATO together, because I believe Putin has had an overwhelming objective since the time he launched 185,000 troops into Ukraine. And that was to break NATO. . . . So holding NATO together is really critical."

"I don't think there is unanimity in NATO about whether or not to bring Urkaine into the NATO family now, at this moment in the middle of a war," he added.

NATO leaders will agree next week to help modernize Ukraine’s armed forces, create a new high-level forum for consultations and reaffirm that it will join their alliance one day, NATO Secretary-General Jens Stoltenberg, the organization’s top civilian official, said Friday. But the war-torn country will not start membership talks soon.

At a two-day summit next week in Lithuania's capital, Vilnius, Stoltenberg insisted that leaders who are a part of NATO "will reaffirm that Ukraine will become a member of NATO and unite on how to bring Ukraine closer to its goal."

Asked when, or how, Ukraine might join, Stoltenberg said that the "most important thing now is to ensure that Ukraine prevails." The U.S., Germany and some other allies consider that Ukraine should not be invited in while it’s at war, so as not to encourage Russia to widen the conflict.

NATO first pledged that Ukraine would become a member, one day in 2008, but things have evolved little since then.

Fox News' Greg Norman and The Associated Press contributed to this report.