Theresa May will meet European Union president Mr Tusk on the sidelines of the Eastern Partnership summit in Brussels.
She will take a leading role at the summit, where she will address delegates on the importance of European unity and security.
And she will also hold private talks on Brexit with Mr Tusk, the president of the European Council.
Arriving in Brussels today, Mrs May said it was time for the UK and the EU to “step forward together”.
She said: “As I say the summit here today is about working with our Eastern partners but of course I will be having other meetings. I will be seeing President Tusk here today talking about the positive discussions, the positive negotiations we are having.
“Looking ahead to the future deepened and special partnership that I want with the European Union.
“These negotiations are continuing but what I am clear about is that we must step forward together. This is for both the UK and the European Union to move on to the next stage.”
Mrs May is likely to offer a new Brexit deal to the EU chief – as well as a host of other payments related to European security.
She could increase her offer of a Brexit divorce bill from €20 billion to €40 billion, including a written breakdown of the country’s obligations.
Until recent days Mrs May was determined not to pay above €20 billion – far below the demands made by Brussels’ leaders.
And the PM’s spokesperson also confirmed Mrs May will confirm the UK will pay millions towards European security – even after Brexit.
Britain will offer £50million to the EU this year to support “reform and security” in eastern Europe, as well as £100m spread over the next five years “to counter disinformation”.
Apart from her talks with Mr Tusk, the Prime Minister will address EU leaders and delegates on European security and unity – and warn of the risk posed to this essential partnership and safety by “hostile states like Russia”.
And she will reiterate her commitment to European security and Britain’s part in Europe – albeit not the EU.
According to Downing Street, she is expected to say: “From agriculture in Ukraine to the tech sector in Belarus – there is a huge amount of potential in the Eastern neighbourhood that we should nurture and develop.
“But we must also be open-eyed to the actions of hostile states like Russia which threaten this potential and attempt to tear our collective strength apart.”
This summit highlights the crucial importance of the European countries working together to protect our shared values and ideals. The UK may be leaving the EU but we are not leaving Europe, and we are unconditionally committed to maintaining Europe’s security.