According to a statement by the Foreign Office, Hague late on Wednesday "made clear that the UK was open to improve bilateral relationship with Iran, on a step-by-step and reciprocal basis".
The statement also added that Hague is willing to meet Salehi in New York in September during the United Nations (UN) General Assembly to bolster relations between the two countries.
The call, which is the first in over a year, came after Iranian Foreign Ministry Spokesman Abbas Araqchi announced the government has sent invitations to European countries, including Britain, to attend the swearing-in ceremony of president-elect Hassan Rohani planned for August 4.
In response, the British Foreign Office said they are not being represented at the ceremony, “as the UK does not have an embassy in Tehran.”
British Shadow Foreign Secretary Douglas Alexander, however, said London’s response to the invitation from Iran “represents both a misjudgment and a missed opportunity".
“Diplomacy involves meeting with people with whom you disagree. The UK should be working with other EU countries to engage with the new Iranian president," he added.
This comes as Jack Straw, the former British Foreign Secretary at Tony Blair’s Labour government, had earlier welcomed the election of Rohani as the new Iranian president saying he has “been urging the [British] government … to reengage with Iranians, because there is a chance now that we can”.
Contradictory reports were on the air about the possible visit of the former British foreign secretary to Tehran, a signal given by the UK to break ice in relations with the Islamic Republic, though his visit is yet to be confirmed.
MRKD/BA