"There should not be any doubt that the United States wants this resolved peacefully, but we are fully prepared for any contingency that Iran creates", Bolton said during a visit to Israel, Iran's enemy in the Middle East.
Bolton said on Thursday that following the USA decision to withdraw from a 2015 global deal aimed at curbing Tehran's nuclear programme, the Trump administration's objective was to "put maximum pressure on the regime" by making sanctions "more extensive and more effective".
"Our objective is that all Iranian forces return to Iran", he adds, saying this is a goal "I think President Putin would share".
"I made it clear that we will not tolerate intervention (in elections) in 2018, and we were ready to take the necessary measures to prevent this", said Bolton.
Patrushev, who also said a broad agreement on restarting contacts between the two countries' army chiefs-of-staff had been reached, said he had invited Bolton and US officials to Russian Federation for future talks, but said no date had been agreed for a follow-up meeting, RIA reported.
Patrushev, according to state-run RIA news agency, said that no statement had been written "because the Americans wanted this to say that we had meddled in their elections, as is their opinion, but we deny this".
Bolton cautioned that 'people who are accused of having violated the sanctions could be indicted, ' alluding to a possible follow-up of the USA indictments of 12 Russian officials as part of an investigation by US special counsel Robert Mueller.
"There won't be any new sanctions if there's no further interference", he said, before specifying that "how we resolve the interference in the past remains to be seen".
Asked if there was any US-Russian understanding about such an operation, Bolton said, "No". The fact of his meeting with Patrushev was, Bolton said, one item the presidents had agreed to in their discussion, as part of an effort to work toward restoring diplomatic and other exchanges.
In the latest signs that the sanctions on Iran are starting to bite, British Airways and Air France both said on Thursday they would be halting flights to Tehran next month.
Donald Trump was elected president as a populist outsider who talked non-intervention, but his administration is being hijacked by neoconservatives who want to preserve the United States empire, former congressman Ron Paul has told RT.
"We are very very early in the process of considering what we are going to do with New START or the INF treaty", he said, referring to the Intermediate-Range Nuclear Forces pact.
Rather, Bolton said that Iran's economy had been mismanaged for years, and the billions Iran received in sanctions relief "mitigated the effects of this management of the economy, and gave the regime new life".