Labour has insisted the party will support the government in any vote to kick start Brexit in an apparent U-turn.
On Saturday Jeremy Corbyn appeared to indicate that his MPs might attempt to block the process in a parliamentary vote if the Prime Minister cannot guarantee British access to the single market.
But on Sunday Labour's deputy leader insisted that the party will support the government in any vote to trigger Article 50, a view echoed by the Labour leader later in the day.
Labour sources confirmed that the party's support for invoking the process was "unconditional" and they would only "seek to amend or influence" the Government's negotiating strategy.
Mr Watson said that the party's MPs "are not going to hold this up" if it comes to a vote in the Commons to formally trigger Article 50.
Mr Watson said he had not discussed the confusion around Labour's position with Mr Corbyn.
"We missed each other on the phone today," he told BBC5 Live's Pienaar's Politics.
"But we are very, very clear we will trigger Article 50 when it comes to Parliament so there is no need for people to be in any doubt about it."
The government had initially hoped to trigger Article 50 without getting any formal assent from MPs.
But the High Court has since ruled that Mrs May does not have the power to begin the process of Brexit unless it comes before Parliament.
Mrs May has said that she will not allow pro-Remain MPs to attempt to hold the proceedings hostage or influence the process of negotiations.
MPs and peers must "accept what the people decided" rather than try to block it, she said.