Russian President Vladimir Putin, right, and President Trump give a joint news conference in Helsinki on July 16. (Pablo Martinez Monsivais/AP)

A bipartisan group of senators has unveiled a comprehensive package of Russia sanctions and measures to counter cybercrime, the latest attempt to push congressional leaders to intensify punitive measures against would-be election hackers ahead of November.

Sens. Lindsey O. Graham (R-S.C.) and Robert J. Menendez (D-N.J.), whose bill is co-sponsored and includes contributions from Sens. Cory Gardner (R-Colo.), Benjamin L. Cardin (D-Md.), John McCain (R-Ariz.) and Jeanne Shaheen (D-N.H.), announced their plans for the legislation last month after President Trump’s widely criticized showing at a summit with Russian President Vladi­mir Putin.

In the weeks since, the clamor from lawmakers and experts to better safeguard the upcoming election has grown more urgent. They point to social media, in particular, as fertile ground for disinformation and influence in campaigns that have proved difficult to police despite the occasional crackdown — such as Facebook’s announcement this week that it had shuttered 32 fake pages .

The bipartisan effort to move sanctions and other legislation through Congress is a sign of lawmakers’ growing frustration with the White House, which has offered mixed messages on Russia’s attempts to manipulate the American electorate and so far declined to fully implement sanctions already at the administration’s disposal.

“The Kremlin continues to attack our democracy, support a war criminal in Syria and violate Ukraine’s sovereignty,” Menendez said in a statement released with the bill. “With the passage of this legislation, Congress will once again act to establish a clear U.S. policy to hold Russia accountable with one clear message: Kremlin aggression will be met with consequences that will shake Putin’s regime to its foundation.”

The administration’s top national security officials — including national security adviser John Bolton, Director of National Intelligence Daniel R. Coats, National Security Agency Director Paul Nakasone, Homeland Security Secretary Kirstjen Nielsen and FBI Director Christopher A. Wray — appeared at Thursday’s White House press briefing to explain their organizations’ collective efforts to counter Russia’s activity.

The bill’s backers face an uphill battle convincing congressional leaders that the moment is ripe for additional sanctions, or any other measures, to counter interference campaigns. Republican lawmakers — including some of those sponsoring this legislation — have been reluctant to commit any more funds to election security in advance of the midterms. And while the Senate’s Foreign Relations and Banking committees have promised to hold hearings on Russian interference and related matters, there are no guarantees that any legislation will emerge, much less make it to a floor vote, in the limited calendar that remains before November.

The sanctions in the proposed package are, as Graham put it, “the most hard-hitting ever imposed” against Russia and other foreign adversaries. They are focused not only on election security, but also on enhancing scrutiny of various Russian money-laundering efforts, containing Russia’s influence internationally, and arming government agencies with better tools to identify and prosecute cybercriminals.

The bill would impose sanctions on any transactions related to Russian energy projects and new Russian sovereign debt, prohibit the issuance of licenses to American individuals and businesses hoping to engage in Russian oil projects, and require title-insurance companies to submit reports on the beneficiaries of high-value real estate deals — a favored haven for wealthy Russians connected to the Kremlin.

The measure would create a new National Fusion Center to Respond to Hybrid Threats, as well as an Office of Cyberspace and the Digital Economy within the State Department, and asks the secretary of state to consider whether Russia should be designated a state sponsor of terrorism. It includes legislation to give prosecutors the ability to shut down botnets and other digital means of targeting critical infrastructure, including elections, as well as to pursue federal charges for hacking voting systems.

The legislation also has a provision to help the United States transfer excess weaponry to NATO countries more quickly, and prohibit the president from withdrawing from NATO without the support of two-thirds of the Senate.