Mrs May invited the leaders of opposition parties to meet with her one-on-one to discuss a way forward.
The Prime Minister told MPs that the Government would continue to work to increase "prosperity, guarantee our security and to strengthen our union" after successful defending a no confidence motion.
She said: "I do not take this responsibility lightly and my Government will continue its work to increase our prosperity, guarantee our security and to strengthen our union.
"We will also continue to work to deliver on the solemn promise we made to the people of this country to deliver on the result of the referendum and leave the European Union."
Labour leader Jeremy Corbyn, raising a point of order after the vote, said: "Last night the House rejected the Government's deal emphatically.
"A week ago the House voted to condemn the idea of a no-deal Brexit.
"Before there can be any positive discussions about the way forward, the Government must remove clearly once and for all the prospect of the catastrophe of a no-deal Brexit from the EU and all the chaos that would come as a result of that."