The UK government is being urged to help provide safe routes out of Afghanistan for people at risk from violence and reprisals by the Taliban.
Labour leader Sir Keir Starmer said there was an obligation to help those who had aided UK forces, and a need to “assert the human rights of everyone”.
Parliament is to be recalled on Wednesday to discuss the situation.
The government says it wants to remove at least 1,000 people a day from Afghanistan and is promising new plans.
US forces have secured the perimeter of Kabul airport, from where hundreds are trying to flee following the Taliban seizing control of virtually the whole country.
But several deaths have been reported amid chaotic scenes.
The United Nations Security Council is meeting on Monday in an effort to avert what has been described as a possible “humanitarian catastrophe”.
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The UK has sent around 600 UK troops to assist the withdrawal.
But many Afghan interpreters and others who have worked with Nato forces in the 20 years since the previous Taliban government was ousted are in fear of their lives.
Speaking on a visit to Wolverhampton, Sir Keir said Mr Johnson had to “step up to the plate and show some leadership, some urgency”.
He added that the UN had to make “an assertion of the human rights of everyone in Afghanistan… particularly women and girls” and reach “an agreement on safe and legal routes for refugees”.