The Taoiseach is trying to persuade a number of EU leaders to accept his plan for a series of protocols or guarantees on issues of concern to Irish voters.
The issues include Irish neutrality, the country's social policy and independence over taxation.
Brian Cowen is attending the two-day summit, where leaders are expected to agree on a series of legally binding assurances to Ireland on the operation of the Treaty.
The Government says that without the guarantees, and a declaration on workers' rights, it would not be in a position to hold a second referendum on the Lisbon Treaty.
How legally binding are the Irish guarantees? Click here
Mr Cowen warned that he would lose a second referendum unless the guarantees promised to Ireland have full treaty force.
He made the appeal in a letter to EU leaders before the summit.
The issue was to be discussed by all EU leaders today in Brussels, but with no prospect of an immediate deal, the question was moved to tomorrow to allow time for a string of bilateral meetings.
Britain and other countries have resisted an Irish push for the guarantees to be enshrined in a treaty protocol, arguing this could encourage Eurosceptics in the bloc to demand the ratification process be started from scratch.
'I need to be able to come out of our meeting and state, without fear of contradiction, that the legal guarantees contained in the decision will, in time, acquire full treaty status by way of a protocol,' Mr Cowen wrote.
'I want to emphasise sincerely, that this is necessary if I am to call, and win, a second referendum,' he concluded in the letter date June 17.
British Prime Minister Gordon Brown told reporters he noted Ireland's concerns and said Britain wanted to 'do the right thing by Ireland and by Europe'.
However, he added: 'I want to ensure that the Lisbon Treaty as it affected Britain will not be changed in any way.'
On his way into the summit, Mr Cowen said he was confident that the Government will receive the reassurances they have sought.
There will also be a non-binding declaration on workers' rights and the rights of governments to organise public services such as schools and health care.
There will also be an Irish national declaration setting out in detail the operation of Irish military neutrality and how that policy works in the context of Europe's common foreign and security policy and the European Defence agency.
Last December, the EU leaders decided that every country will keep a full-time member of the European Commission if the Lisbon Treaty comes into force.
Taken together, the Government believes that these guarantees, declarations and decision will provide it with enough justification for holding a second referendum on the Lisbon Treaty.
