The Labour leader made the pledge on a visit to Belfast, where he met with political leaders including Colum Eastwood.
His trip, which also involved meetings with Irish government ministers in Dublin, came amid the row over the post-Brexit trading arrangements.
The Government has said it will table legislation on Monday that will give ministers powers to scrap parts of the protocol.
The Bill, due to come before Parliament next week, will see the Government move without the consent of the EU to change the terms of the international treaty in a bid to reduce the checks on the movement of goods across the Irish Sea.
The EU has made clear that such a step would represent a breach of international law that could prompt retaliatory action.
Sir Keir said the focus should be on achieving a negotiated settlement to resolve issues with the protocol’s implementation.
“We would scrap the legislation, and I think there has been an impasse in the negotiations because we haven’t seen the high levels of trust that we need for negotiations like this, not least from our prime minister,” he told reporters in Belfast.
“But also we need give and take on both sides — the EU, as well as the UK.
“I do not think that the remaining issues cannot be resolved with a different approach, with that high level of trust, with an honest broker prime minister getting people around the table and negotiating what needs to be negotiated.”
Sir Keir also confirmed that his party would vote against the legislation at Westminster.
“We think that it is the wrong approach,” he said.
“I’m not pretending there aren’t issues and challenges with the protocol, of course there are.
“We have been listening to the political parties here, to communities, to business groups.
“I think that those challenges can be overcome around the negotiating table with statecraft, with high levels of trust.”