Conservative leader Kemi Badenoch accused the prime minister of “dithering” on Jackdaw and said a ban on new oil and gas licences should be repealed.
However, Burnham said her party had “messed up” the original decision by not giving any regard to climate obligations – things he said “have to be considered in the round”.
Energy Secretary Miatta Fahnbulleh said gas from Jackdaw would be in homes and businesses this month, but that it would not lower energy bills this winter.
She said the decision was “compatible” with legally binding climate commitments, adding: “We remain resolute in ending new licences for oil and gas and achieving net zero by 2050.”
Environmental groups have criticised the Jackdaw approval. Areeba Hamid, the co-executive director of Greenpeace, said it was “the wrong decision” in terms of lowering energy bills, providing energy security, and addressing climate change.
Meanwhile, Oxfam said the government had “drilled straight through the UK’s climate commitments”.
During their Friday talks, Trump and Burnham spoke about the Falkland Islands and the Sea Lion oilfield project, a joint venture between British and Israeli companies.
In September, the Argentinian government threatened to impose economic sanctions on firms exploiting oil close to the Falkland Islands, and earlier this month, it began legal action to stop the exploration of oil and gas fields.
Burnham raised the “economic consequences of Argentina’s coercive measures for the UK and US and reiterated the importance of respecting the Islanders’ right to develop their natural resources”, Downing Street said.
The two leaders also discussed Ukraine, with the prime minister underlining the importance for Ukraine “to have full access to Starlink so they can continue to defend themselves against Russia’s full-scale invasion”, according to Number 10.
Starlink technology is a satellite system owned by Elon Musk’s SpaceX company which Ukraine has relied upon during the war.
In recent days, Ukraine has been recording issues with the network, according to sources within the defence ministry. This has affected the country’s ability to use attack drones and co-ordinate defensive operations.
The Downing Street statement added: “The Prime Minister recognised the work of President Trump to bring Putin to the negotiation table and the leaders agreed to work together, alongside international partners to bring an end to the bloodshed.”