Environmental campaigners and Green Party leader Zack Polanski have both separately written to Andy Burnham and the foreign secretary to raise concerns about Rosebank's links to an Israeli company, Delek Group.
Last year Delek Group was included in a UN database of firms which allegedly provide services or utilities to support settlements in occupied Palestinian territories.
A spokesman for the company told the Daily Telegraph, external it no longer had any involvement in Israeli settlements and was wrongly included in the database.
Delek Group controls Ithaca Energy, which holds a 20% stake in Rosebank.
The campaign group Uplift, whose legal challenge against the Rosebank project in 2023 led to the ongoing delay over a decision on exploration, has helped organise a letter to Burnham and Foreign Secretary Ed Miliband.
In a letter seen by BBC News, campaigners from Stop Rosebank and Greenpeace, with assistance from Uplift, have asked the government to clarify whether Delek will fall foul of the sanctions announced last month.
Separately, Polanski has also written to Miliband, asking what steps the government would take to make sure revenue from UK oil and gas production did not finance illegal settlements.
He said: "Rosebank is a test of whether Labour's proposed sanctions regime is fit for purpose.
"Companies blacklisted by the UN for operating in the illegal settlements should not be financed by oil and gas revenues from the North Sea."
Last month, Miliband signalled a hardening of the UK's position when he announced action against companies and individuals who provide services such as infrastructure to settlement expansion.
The UK sanctions will also ban imports of goods from illegal settlements.
In its letter to Burnham, Uplift asked him to "confirm, unequivocally, whether Delek will be caught by the new planned measures".
They added: "If it is not, please explain how that is consistent with the government's stated intent to sanction those who finance or facilitate illegal settlements?"
A spokesperson for Ithaca Energy told the BBC: "Ithaca Energy is a London Stock Exchange listed company which is a member of the FTSE 100, and which is governed by the highest standards of corporate governance.
"Ithaca is one of the biggest investors in the North Sea and Scotland, is a responsible employer and is a major contributor to both the UK Treasury through tax payments and to the UK's energy security."
A spokesman for Delek Group told the Telegraph: "Delek Group has been wrongly included in the UN database.
"Together with our legal advisers, we intend to formally challenge this and request the immediate removal of our name from the UN database."
The question of whether to approve Rosebank, as well as the Jackdaw gas field east of Aberdeen, has become hugely politically significant.
Rosebank was approved by the previous Conservative government in 2023, but that decision was successfully challenged in the courts by campaigners including Uplift.
The decision now lies with the Energy Secretary Miatta Fahnbulleh, but will be seen as an important indication of Burnham's wider thinking on oil and gas.
Miliband was widely thought to have been opposed to Rosebank when he served as Sir Keir Starmer's energy secretary.
Burnham has spoken repeatedly of the need for a "flexible" approach to energy and is believed to be in favour of drilling more where licenses already exist in the North Sea.
The decision could also have implications for the relationship between the UK and the US. President Trump has placed pressure on successive UK prime ministers to drill more in the North Sea.
While Downing Street is relieved that Trump has not lashed out at the government's recent West Bank sanctions, his administration has said the US will not take the same course of action.
Tessa Khan, executive director at Uplift, said "not one penny of North Sea oil profits" should go to a company which "itself now risks being sanctioned by the UK".
The Foreign Office declined to comment.
Israel has built about 160 settlements housing 700,000 Jews since it occupied the West Bank and East Jerusalem during the 1967 Middle East war. An estimated 3.3 million Palestinians live alongside them.
Settlements are illegal under international law, and there has been a rise in violence towards Palestinians in the West Bank by settlers in recent months.
Israel has criticised the UK sanctions, accusing the government of "anti-Israel policies". %!s()
