The controls on steel imports were due to end this week.
Boris Johnson was asked if this could lead to a possible violation of international law.
The proposed approach was set out on Thursday.
The final decision has not been made, according to the department.
Mr Johnson said that keeping the import controls on foreign steel would protect British producers from rising energy prices.
British steel needs to be given with cheaper energy.
I think it's reasonable for UK steel to have the same protections that other European steel economies do.
The resignation of Mr Johnson's ethics adviser Lord Geidt was linked to disagreements about steel tariffs.
The far wider scope of Mr Geidt's objection was not reflected in the interpretation of his decision to quit.
In response to tariffs imposed by the Trump administration, the European Union introduced limits on steel imports. After the UK left the EU the controls were mirrored.
The steel safeguards are meant to protect the domestic market from cheap steel coming from overseas.
There are controls in place for 15 different types of steel. There are import limits on five categories that are set to expire on June 30th.
Extending tariffs on steel imports is seen as breakingWTO commitments.
Brandon Lewis said the government was focused on "ensuring we work within international law."
The Northern Ireland Secretary said that he was not saying the government was going to do this, but that it was something that was supported across the sector and the government needed to get the balance.
There would be no legitimate reason to challenge the extension of the steel controls, according to UK Steel.
The Department for International Trade is consulting with foreign counterparts in order to make a final decision on whether to extend the safeguards.
According to UK Steel, ending the import controls would expose British steelmakers to a distorted global marketplace and that could cause as much as £150m a year in damage.
David Lammy said Labour would back the prime minister in the tariffs being continued.
He said that the EU and the Americans had continued with the extension so they would support him.
The unions support him, the industry supports him, and the Labour Party supports him.
Tom Tugendhat, the chairman of the Foreign Affairs Select Committee, said protectionism is destructive. The tariffs are a tax on consumers.