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.
The senior USA official told reporters that they discussed "the whole range of issues", like non-proliferation and arms control, bilateral issues, the fight against terrorism, illegal migration, topics related to cyberspace, regional issues such as Syria, the Middle East, Afghanistan and Ukraine.
"I think the effects, the economic effects certainly, are even stronger than we anticipated", Bolton said.
Sanctions that the USA reimposed on Iran have been more effective than expected, though regime change there is not part of Washington's policy, President Donald Trump's national security adviser said on Wednesday.
John Bolton, a noted foreign policy hawk who became Mr Trump's national security adviser in March and is in Jerusalem for talks with prime minister Binyamin Netanyahu, appeared to rule out chances of a swift U.S. withdrawal from Syria, as previously demanded by his boss.
"The Iran nuclear deal mitigated the effects of its mismanagement of the economy and gave the regime new life", Bolton said.
Bolton hosts a press conference after meeting with Russia's Nikolai Patrushev for five hours.
"I think there's been a lot of progress in relations in the region as a result of the process of going through the possible outlines of what the plan would look like", he said.
In a new development, he also said the United States will cut funding for the U.N. human rights office, where former Chilean President Michelle Bachelet is set to become the new High Commissioner for Human Rights next month. USA presence in Syria has no basis in either domestic or worldwide law, while Russian and Iranian troops operate at the invitation of the government in Damascus.
Critics of the nuclear agreement, including Israeli Prime Minister Benjamin Netanyahu, say Iran got too much while giving up too little and retained an ability to pursue nuclear weapons.
"That's a possibility", Bolton said of the Moscow Treaty.
Bolton said the nuclear deal, signed in 2015 under former president Barack Obama's administration, gave the Iranian regime "new life" with the outcome of "increased belligerency in the region".
Commenting on Bolton's demand that Moscow pressure Iran into getting its troops out of Syria, Paul said that while this was a "reasonable request", it should rather apply to "any foreign nation that has troops in Syria that haven't been invited". Patrushev also said he conveyed an invitation to Bolton and other United States officials to visit Russian Federation for additional talks in the future.