Foreign Secretary William Hague has held his first meeting with his Iranian counterpart Mohammed Javad Zarif since President Hassan Rouhani was elected, BBC reported.
A series of talks are taking place at the United Nations amid signs of a thaw in Iran's relations with the West.
The UK shut down its Tehran embassy in 2011 after it was stormed in a protest over British nuclear sanctions.
Mr Hague welcomed recent statements from Iran aimed at easing concerns about its uranium enrichment work.
Last week President Rouhani, who was elected in June, said he was ready to restart stalled talks on the issue after stating that his country would never seek to build nuclear weapons.
Mr Hague said those statements should be matched "by concrete steps by Iran to address the international community's concerns about Iran's intentions".
He added: "The United Kingdom does not seek a confrontational relationship with Iran and is open to better relations.
"The United Kingdom welcomes President Rouhani and Foreign Minister Zarif's recent statements about Iran's wish to improve its relations with the outside world."
Iranian students stormed the Tehran embassy in November 2011 following Britain's decision to impose further sanctions on Iran over its nuclear programme as a result of a report by the UN's nuclear watchdog.
UK diplomatic staff were withdrawn from Iran and Iranian diplomats were expelled from London in the wake of the incident.
Mr Hague said that as well as Iran's nuclear programme, his discussions with Mr Zarif took in the conflict in Syria, human rights and bilateral relations between the two countries.
He added: "We talked about the need for peace in Syria, where Iran could play a constructive role, including by supporting the Geneva framework for a negotiation between the Assad regime and the opposition and stopping its direct support for regime forces.
"And while welcoming recent announcements on the release of some political prisoners, I raised our concerns about human rights in Iran."
The meeting between Mr Hague and Mr Zarif is not the first time he has held talks with his Iranian counterpart since 2011. He saw Ali Akbar Salehi - foreign minister under the former President, Mahmoud Ahmadinejad - in the margins of the Heart of Asia Conference in Kabul in June 2012.