Tom Watson said Labour's immigration policy was unclear as he shed light on his sometimes strained relationship with Jeremy Corbyn's top team.
Labour's deputy leader said the party wants to see a fair immigration policy implemented post-Brexit but suggested it was difficult to set out detailed plans before Theresa May reveals her negotiating hand.
Mr Watson's comments come as senior Labour MPs call on Mr Corbyn to put pressure on the Prime Minister to pursue a two-tier immigration system.
When told on the Sophy Ridge On Sunday show on Sky News that Labour's immigration policy was unclear, Mr Watson said: "Well, I think you have got a fair point on that and it centres around this debate around free movement of labour which is one of the treaties we are signed up to currently in the EU."
He added: "We want a fair immigration system. It's unfair of you to ask what Labour's notional position is when we don't even know what Theresa May's negotiating position is that's on free movement."
Mr Watson also set out the state of his relationship with Mr Corbyn.
He said: "There were teething problems with the way Jeremy's team work and I don't have a great relationship with some of his team members and that's probably on record.
"But with Jeremy himself we enjoy a very strong relationship."
Mr Watson also said he is "very clear" that Mr Corbyn will lead Labour into the 2020 general election while ruling out talk of electoral alliances as a "counsel of despair".
The Labour MPs Emma Reynolds and Stephen Kinnock have urged Mr Corbyn to press Mrs May to introduce a two-tier immigration system split between high-skilled and low-skilled workers coming to the UK from the EU.