Senate Republicans have twice blocked legislation aimed at strengthening US election security in the 24 hours since the former special counsel Robert Mueller warned that Russian election interference was happening “as we sit here”.

Since Mueller left the witness stand on Wednesday, Republican senators have blocked a House-backed bill and a separate trio of bills meant to beef up US election security.

The Senate Democratic leader, Chuck Schumer of New York, accused Republicans of having “buried commonsense election security bills in their legislative graveyard”. He pledged to keep putting forward requests to vote on legislation, including a House-passed bill that would authorize $775m in grants over the next two years to help states secure their voting systems.

The Senate majority leader, Mitch McConnell, however, criticized the House bill as “so partisan it received just one Republican vote over in the House”, asserting that any election security proposal must be bipartisan.

The developments come as a new report, released Thursday by the Senate intelligence committee, found that the Russian government directed “extensive activity” against US election systems ahead of the 2016 presidential election. The report also said that states hadn’t been appropriately warned of the threat against their systems and warned many of them still had outdated voting machines.

During his Wednesday testimony, Mueller, speaking of findings from his team’s investigation into Russian meddling, emphasized the issue was not limited to the 2016 election. “It wasn’t a single attempt. They’re doing it as we sit here,” Mueller said. “And they expect to do it during the next campaign.”

The election security report is the first chapter of several volumes that the committee is expected to release in its investigation of Russian election interference. The panel issued recommendations for election security in May 2018 and is now issuing a complete volume of its findings.

The nation’s intelligence chiefs say Russia remains intent on disrupting US elections after attempting to breach the election systems of 21 states in 2016. There is no evidence that any votes were changed.

McConnell, a Kentucky Republican, has said federal officials are making strides at improving election security. Republicans are saying no new money is needed immediately.