In the early hours of June 20, the Islamic Revolution Guards Corps (IRGC) Aerospace Force shot down a USA unmanned aerial vehicle (UAV) that intruded into the airspace of Iran.
Reiterating comments made by Trump, Bolton said: "our military is rebuilt, new and ready to go - by far the best in the world".
USA ally Israel, which has itself long threatened strikes against Iran's disputed nuclear programme, signalled understanding for Trump's stance given his campaign of diplomatic pressure on Tehran.
The United States left the multilateral nuclear agreement with Iran last May and imposed heavy sanctions on Iran, particularly targeting its oil exports and global banking, the two areas Europe has helped to help Iran with.
"This visit has provided an important opportunity for open, frank and constructive engagement with the Iranian Government", said Dr Murrison, following talks with the Iranian government this weekend. "They know precisely how to find us".
Javad Zarif tweeted that the presidential adviser was "moments away from trapping" Trump into a "war", before the US president called off the strikes against Iran.
Iran's foreign minister said Bolton was trying to force the US into a conflict with Iran.
Bolton, known as one of the most hawkish senior members of the administration, arrived in Israel on Saturday to attend a tripartite meeting Tuesday of the national security advisers of the US, Israel and Russian Federation.
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Meanwhile, U.S. national security adviser John Bolton was in Jerusalem on Sunday, where he said Iran should not "mistake U.S. prudence and discretion for weakness". Trump said he backed away from the planned strikes after learning that about 150 people would be killed, but he said the military option remained.
Bolton's tough message seemed to be aimed not only at Tehran, but also at reassuring key US allies that the White House remains committed to maintaining pressure on Iran. "No one has granted them a hunting license in the Middle East", Bolton said during a visit to Israel.
Any conflict in the Gulf region may spread uncontrollably, a senior Iranian military commander was cited as saying on Sunday by the semi-official news agency Fars. He was quoted by the official IRNA news agency.
On top of that, Vice President Mike Pence told CNN on June 23 that the administration remains doubtful that the drone attack was authorized "at the highest levels", of Iran's leadership. Nevertheless, traditional business models are no longer sustainable and high-quality publications, like ours, are being forced to look for new ways to keep going.
Murrison said he had also pressed again on behalf of the British government for the "urgent and unconditional release" of British-Iranian aid worker Nazanin Zaghari-Ratcliffe.
Murrison said he reiterated Britain's determination to maintain the nuclear deal Iran signed with world powers in 2015 during his talks with government representatives, including Vice President Masoumeh Ebtekar, Deputy Foreign Minister Abbas Araghchi and the Deputy Head of the Atomic Energy Organisation of Iran Behrouz Kamalvandi.
In response to the shooting down of the drone, US President Donald Trump ordered US military cyber forces to target Iranian military computer systems on Thursday.
"Iran used those hundreds of billions of dollars to fund empire building, not nation building", he continued, warning that the Islamic Republic is "devouring one state after the other".