May had been due to hold the vote later on Tuesday, but on Monday announced she would defer it and seek extra reassurances from the European Union to make sure it got through parliament, Reuters reported.
May is looking to resolve the impasse over her deal as quickly as possible, and intends to get the assurances she needs from European leaders before Jan. 21, the spokesman told reporters.
He also said May had earlier held a productive meeting with Dutch Prime Minister Mark Rutte, the first stop on a tour of European capitals. The two agreed to work to find a way through the current situation, he said.
May will hold a meeting of her cabinet on Wednesday afternoon.
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