The British prime minister vowed on Tuesday to protect the rights of Iraq's Kurdistan region within the boundaries of the Iraqi constitution.

Theresa May held a phone call with Kurdish prime minister Nechirvan Barzani that underlined Britain's continued support for Iraq's Kurdistan Regional Government (KRG).

Baghdad and Erbil have quarrelled over territory and oil revenue sharing since the fall of Saddam Hussein in 2003. But tensions reached boiling point after the autonomous Kurdish region decided to hold a vote on Kurdish independence in late September.

The vote was declared illegitimate by Iraq's central government, although voters in the autonomous Kurdish region and Kurdish-held areas elsewhere overwhelmingly backed secession.

"The UK [will] continue to fight to protect the identity and rights of the Kurdish people under the Iraqi constitution," a Downing Street spokesperson said on Tuesday.

Mrs May reiterated the UK’s continued respect for the territorial integrity and unity of Iraq, whilst maintaining the importance of holding dialogue and negotiations to solve the issues between Baghdad and Erbil, the capital city of Kurdistan.

The British prime minister and Mr Nechirvan agreed on the importance of negotiating an agreement over federal control, joint management of the borders and a resumption of international flights to Kurdistan’s airports in Erbil and the city of Suleimaniyah.

"They both said that they hoped to see progress on this soon," the Downing Street spokesperson said.

In response to the Kurdish independence referendum in September, Baghdad unleashed an economic barrage against the KRG by halting all international flights in and out of the autonomous region, and launched a military operation that recaptured the oil-rich city of Kirkuk and other disputed areas held by Kurdish forces. These disputed areas lie outside of the autonomous Kurdish region but are claimed by both Baghdad and Erbil.

Neighbouring Turkey and Iran have also threatened to close their borders with Kurdistan to oil exports.

In November, the Iraqi Federal Supreme Court ruled that the Kurdish independence referendum was unconstitutional and the results void, prohibiting the region from seceding. This move strengthened Baghdad’s hand in its stand-off with the Kurdish region.

In response, the KRG said it would respect the Supreme Court's ruling, which declared that no Iraqi province could secede from Baghdad.

The British prime minister on Tuesday welcomed the KRG’s recognition of the Supreme Court’s ruling that Iraq is unified and indivisible.

Meanwhile, Mrs May invited Mr Barzani, the Kurdish prime minister, for talks in London.

"The prime minister said she would be pleased to see prime minister Barzani in London in due course to make further progress on these matters," the Downing Street spokesperson said.