In the Commons, Badenoch said the US was the UK’s single biggest trade partner and warned the prime minister he would need to “look after the special relationship”.
She said there was now a “risk of increased tariffs on UK exports” and asked if he would bring back talks on establishing a free trade agreement with the US.
Since leaving the European Union, UK ministers have been keen to reach a trade deal with the US – however, there has been little progress.
During his election campaign, Trump pledged to dramatically increase tariffs on foreign exports.
Replying to Badenoch, Sir Keir said: “Of course we will discuss issues of our economy with the president-elect, as we already have done.”
On defence, the Conservative leader echoed calls from Trump that European countries should increase their defence spending and urged the prime minister to match her party’s commitment to raise defence spending to 2.5% of GDP by 2030.
Sir Keir reiterated his government’s commitment to the 2.5% target – although it has not set a deadline for meeting the goal.
He added that, unlike the previous Labour government, the Conservatives had failed to meet the target whilst in office.
He also attacked the Conservatives for leaving a £17bn black hole in the Ministry of Defence’s finances.
Labour accused Badenoch of misleading Parliament when she incorrectly told MPs that the “chancellor’s Budget did not even mention defence”.
Badenoch’s spokesman insisted she had not got it wrong because it was “obvious” from the context of what she had said in her previous question that “she was referring to the fact that there was no reference to how Labour intend to get to that 2.5%”.
In her Budget speech last week, Chancellor Rachel Reeves said “we will set a path to spending 2.5% of GDP on defence at a future fiscal event.”