Foreign Secretary Jack Straw has already flown abroad to Luxembourg to attend his first meeting of EU foreign ministers.
Top of the agenda will be the decision of the Irish people to reject the Nice treaty in a referendum.
The treaty provides for further expansion of the European Union.
New line up
Meanwhile the prime minister is set to complete the line-up of his new government.
Mr Blair is believed to have spent the weekend drawing up a list of his junior ministerial team.
He will telephone the successful MPs and peers on Monday before making their identities public.
It follows Friday's cabinet reshuffle and is part of Labour's plan to be seen to be hitting the ground running in the immediate aftermath of last week's poll.
The shake-up in the junior ranks will be closely watched.
Speculation is mounting that Europe Minister Keith Vaz is set to return to the backbenches.
Mr Vaz was discharged from hospital on Monday after spending the weekend in Leicester Royal Infirmary recovering from an infection.
He went on sick leave after collapsing following a television interview in March.
Some newspaper reports have suggested that Mr Vaz will return to the backbenches, with Downing Street attributing the move to his poor health.
There is speculation that Mr Blair has decided to appoint Lord Macdonald, transport minister in the last parliament, as the government's "enforcer" based at the Cabinet Office.
Newspaper reports at the weekend also predicted enhanced powers for Lord Falconer at the same office, and a new post for Health Minister John Denham.
Baroness Symons, a minister at the Ministry of Defence, could also be promoted.
And commentators will be watching closely to see if Shaun Woodward, the former Tory frontbencher, will be given a ministerial job.
Meanwhile, many of the new cabinet members have been touring media studios to outline Labour's plans.
There are also first signs of the Conservative leadership campaign getting underway.
Ann Widdecombe, shadow home secretary, told BBC's Breakfast with Frost programme that several people had pressed her to stand and she was now trying to gauge the breadth of support.
"There are quite a lot of people who would like me to run but that does not mean I can just jump in," she said.
Former party chairman Chris Patten underlined the need for the party to come together, telling the same programme that the Tories "must be a broad church and not a narrow sect."