The remaining 27 EU member states have stated they want the future UK-EU relationship to include “ambitious provisions” for movement of citizens between Britain and the bloc.
But, Ms Rudd signalled the Cabinet have yet to agree whether or not to negotiate with Brussels on future immigration rules during Brexit talks.
Although Brexit negotiations are likely to be concluded in October this year, Ms Rudd also confirmed the Government will not be presenting their post-Brexit immigration plans to Parliament until “the end of the year”.
She told MPs the Government will wait until the conclusions of a final Migration Advisory Committee report in September.
The Home Secretary also refused to commit to the Government’s target of reducing net migration to the UK to below 100,000 by 2022.
The revelations came in a bruising exchange between Ms Rudd and Labour MP Yvette Cooper, the chair of the House of Commons Home Affairs Select Committee.
It has been suggested offering more favourable immigration rights to EU citizens after Brexit could allow Britain to negotiate greater access to the bloc’s markets.
Asked by Ms Cooper whether the Cabinet has a view on whether immigration will form part of negotiations on the future EU-UK partnership, Ms Rudd replied: “It’s for the Prime Minister to decide what the state of the negotiations are going forward.
“We’ve achieved a lot in the past few months and going forward it’s going to be for the Prime Minister to decide.”
When Ms Cooper suggested that means there is “no Government proposal on even whether or not immigration is going to be included in the discussions”, Ms Rudd said: “You can take it as you want.”
At last week’s European Council summit, the EU27 adopted guidelines for upcoming negotiations on the future UK-EU relationship.
They stated: “The future partnership should include ambitious provisions on movement of natural persons, based on full reciprocity and non-discrimination among Member States, and related areas such as coordination of social security and recognition of professional qualifications.”
When these were put to Ms Rudd by Ms Cooper, the Home Secretary commented: “It will be up to the Prime Minister and [Brexit Secretary] David Davis to decide to what level they decide to engage with that.”
Ms Cooper said: “The problem is you have got a net migration target on one hand, you have got some unknown hidden objectives in the negotiations on the other, but none of us have any idea what they are.
“Do you think you are remotely being honest and open with the public about what future immigration policy and reality will be?”
Ms Rudd replied: “I think what the public want is to make sure they have a Government that is committed to reducing the high numbers of net migration, and they are seeing that with this Government.”
Ms Rudd was also questioned on whether she is still aiming to meet the Government’s net migration target by the end of this parliament, to which she replied: “I’m still focused on making sure we reduce net migration to sustainable levels.”
When challenged, the Home Secretary did not clarify whether that was a “yes or no” answer to the tens of thousands target.
In her appearance before MPs, the Home Secretary also announced a new recruitment drive for 1,000 border staff “to improve the quality of our border and prepare specifically for Brexit”.
This comes on top of 300 new posts announced in October last year.
Although the Home Office could not confirm how many of the 1,000 positions to be advertised will be new roles – rather than to cover upcoming vacancies over the next few months – the recruitment drive is aimed to make sure the Border Force has the staff it needs by the time Britain leaves the EU in March next year.