MPs today began two days of debate on the second reading in the House of Commons of the European Union (Notification of Withdrawal) Bill.
If passed, the Bill will hand Theresa May the authority to trigger Article 50 of the Lisbon Treaty and start EU divorce talks.
The Prime Minister has vowed to invoke Article 50 by the end of March.
Brexit Secretary David Davis began proceedings by asking MPs: "Do we trust the people or not?"
But, despite the June 23 vote to quit the EU, Sir Keir responded by claiming the Article 50 Bill is "very difficult" for Labour.
He said: "We have before us a short Bill and a relatively simple Bill. But for the Labour Party this is a very difficult Bill."
Sir Keir Starmer admitted Article 50 is 'difficult' for Labour
We have before us a short Bill and a relatively simple Bill. But for the Labour Party this is a very difficult Bill.
Sir Keir Starmer
Sir Keir's comments sparked laughter on the Conservative benches, with the shadow Brexit secretary forced to ask Tory MPs to "be courteous as I try to set out the position of the Labour Party in what are very difficult circumstances".
He added: "We are a fiercely internationalist party, we're a pro-European party. We believe that through our alliances we achieve more together than we do alone.
"We believe international co-operation and international collaboration and we believe in the international rule of law. These beliefs will never change."
Labour leader Jeremy Corbyn has ordered his MPs not to block Brexit but could face a rebellion by up to 100 pro-Remain MPs.
Mr Corbyn will try and introduce seven amendments to the Article 50 Bill at a later date in the Bill's progress through Parliament.