Senate Republican leaders are under pressure from GOP lawmakers with presidential ambitions to join the House in investigating the 2012 Benghazi attack.

Sens. Ted Cruz Rafael (Ted) Edward CruzMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (R-Texas), Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) and Marco Rubio Marco Antonio RubioSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Florida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Fla.), three young rising conservative stars who are weighing 2016 bids, say the Senate should participate in a joint investigation with the House.

ADVERTISEMENT

“The House is doing its job and engaged in oversight. For six years under [Senate Majority Leader] Harry Reid Harry Mason ReidDemocrats fear Russia interference could spoil bid to retake Senate Graham signals support for confirming a Supreme Court nominee this year Trump signals he will move to replace Ginsburg 'without delay' MORE [D-Nev.], the Senate has refused to do its job. I am hopeful and optimistic the Senate will finally begin meaningful oversight. That is its constitutional responsibility,” Cruz told The Hill.

But Sen. John McCain John Sidney McCainMomentum growing among Republicans for Supreme Court vote before Election Day McConnell urges GOP senators to 'keep your powder dry' on Supreme Court vacancy McSally says current Senate should vote on Trump nominee MORE (R-Ariz.), who is set to take over as chairman of the Armed Services Committee, has yet to decide whether the Senate needs to deploy its investigate resources while the House is already doing so.

“What we need to do is talk with the House guys, see where they are and see if they think it’s helpful,” McCain said when asked whether the Senate should launch an investigation. “I’ll be guided by that.”

The 2008 presidential nominee has been discussing his options with Rep. Trey Gowdy Harold (Trey) Watson GowdySunday shows preview: Election integrity dominates as Nov. 3 nears Tim Scott invokes Breonna Taylor, George Floyd in Trump convention speech Sunday shows preview: Republicans gear up for national convention, USPS debate continues in Washington MORE (R-S.C.), the chairman of the House Select Committee on Benghazi.

A House GOP aide said the decision about whether the Senate participates is up to the leadership, including McCain and other incoming Republican leadership. Meanwhile, Gowdy has directed his panel to continue moving forward with its investigation.

The South Carolina congressman has scheduled a hearing for December although the date and witness list has yet to be determined. He has also laid out an intensive investigative plan for 2015 that will include multiple hearings early in the year — some open to the public and others behind closed doors.

Cruz introduced a resolution last year calling on Congress to create a joint Senate-House committee to investigate Benghazi.

Paul, Rubio and 23 other Senate Republicans co-sponsored the measure — including Senate Republican Whip John Cornyn John CornynCalls grow for Biden to expand election map in final sprint Bipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection MORE (Texas) but not Senate Republican Leader Mitch McConnell Addison (Mitch) Mitchell McConnellOcasio-Cortez to voters: Tell McConnell 'he is playing with fire' with Ginsburg's seat McConnell locks down key GOP votes in Supreme Court fight Video shows NYC subway station renamed after Ruth Bader Ginsburg MORE (Ky.).

Aides to Paul and Rubio on Friday said their bosses believe the Senate should join the House select committee.

Rubio earlier this year criticized the Senate Foreign Relations Committee, which he sits on, because it had “not even attempted to conduct a thorough investigation into these terrorist attacks that took the lives of four brave Americans.”

The House Intelligence Committee released a report Friday that largely exonerated the Obama administration of Republican charges that it had covered up the circumstances of the attack and intentionally mislead Congress.

Democrats argue the latest House findings call into question the need for further investigation.

“Serious investigations have shown that the administration acted appropriately in Benghazi. Sen. McCain should think twice before throwing even more taxpayer dollars into what amounts to a baseless partisan stunt,” said a Senate Democratic aide.

The House intelligence panel, chaired by retiring Republican Rep. Mike Rogers (R-Mich.), found the administration did not intentionally mislead the public when Susan Rice, the U.S. ambassador to the United Nations, used talking points describing the attack as “spontaneous” and “not premeditated.”

The GOP-controlled panel also concluded “there was no stand down order issued” to the military that stopped it from intervening in the attack.

A spokesman for the House Select Committee on Benghazi said it has reviewed the Intelligence Committee’s report “along with other committee reports and materials as the investigation proceeds.”

Sen. Lindsey Graham Lindsey Olin GrahamMcConnell locks down key GOP votes in Supreme Court fight Will Republicans' rank hypocrisy hinder their rush to replace Ginsburg? Momentum growing among Republicans for Supreme Court vote before Election Day MORE (R-S.C.), McCain’s closest ally in the Senate, attacked the House report Sunday as “full of crap.”

"I don't believe that the report is accurate, given the role that Mike Morell played in misleading the Congress on two different occasions. Why didn't the report say that?" he told CNN’s “State of the Union” in an interview Sunday, referring to the deputy director of the Central Intelligence Agency at the time.

He argued that when Rice went on television after the attack she said on three occasions the consulate was strongly, secured when “nothing could be further … from the truth.”

“She gave an impression to the American people that these folks were well taken care of, when it was in fact a death trap. Who told her to say that?” he said, describing the House report “a complete bunch of garbage.”

Graham, who has floated a White House bid of his own, said last week the Senate needs to investigate.

“What I would envision is a select committee being formed in the Senate of members from the appropriate committees instead of a stovepipe approach,” he told conservative radio host Hugh Hewitt.

“We would create a select committee in the Senate to marry up with the select committee in the House, become a joint select committee, bootstrap on the work already done by the House, and take this to its logical conclusion,” he added.

The attack killed Christopher Stephens, the U.S. ambassador to Libya, two months before the 2012 presidential election and became a vulnerability for President Obama in the campaign.

Evidence that the State Department mishandled security before the attack, botched its response or tried to hide mistakes would become an issue in the 2016 campaign if Hillary Clinton Hillary Diane Rodham ClintonBiden leads Trump by 36 points nationally among Latinos: poll Democratic super PAC to hit Trump in battleground states over coronavirus deaths Battle lines drawn on precedent in Supreme Court fight MORE, who served as secretary of State at the time, runs for the White House.

Paul, a leading 2016 contender, has repeatedly criticized Clinton for not taking the security situation in Libya more seriously.

He argues that if “she cannot protect our embassies” it “precludes her from ever being considered as commander in chief.”