The French and German leaders are meeting in Berlin to try to narrow their differences over economic policy ahead of an EU summit on Thursday.
Chancellor Angela Merkel was initially expected to meet French President Nicolas Sarkozy last week. The delay fuelled speculation about a big rift.
Correspondents say France is keen to launch regular summits of eurozone leaders, but Germany is wary of that.
Germany wants EU countries that pile up debts to face sanctions.
EU leaders are anxious to avoid having to rescue another member state, following the emergency bail-out for debt-laden Greece. There are continuing fears that the Greek crisis could undermine other heavily indebted eurozone countries.
Governments across the EU face the challenge of imposing unpopular spending cuts while not stifling growth.
On Thursday the President of the European Council, Herman van Rompuy, will brief EU leaders on the work of an EU task force on economic governance, which he is chairing.
In Berlin last week he said that Mrs Merkel "shares the principal directions to strengthen budgetary discipline through the [EU] Stability Pact and to reduce the divergences in competitiveness between the member states".
He appeared to distance himself from the French idea of having a new "secretariat" to co-ordinate economic policy in the 16-nation eurozone.
"We do not need new institutions to meet our goals. We need more effectiveness," Mr Van Rompuy said, stressing the need for "preventive action to avoid countries accumulating excessive deficits".
"We will be tougher in correcting deficits with more rules-based and semi-automatic sanctions."
In an interview on BBC Radio 4's Today programme, French Finance Minister Christine Lagarde said "we must play by the rules and the rules have to be changed".
The UK and some other member states are sceptical about an EU plan to subject national budgets to EU "peer review" before they are debated by national parliaments.
Ms Lagarde played down such differences on Monday. She said there was a need to "share and agree on macro-economic data and forecasts - I don't see that as a major obstacle".
Mrs Merkel and Mr Sarkozy have jointly urged the European Commission to speed up measures to tighten financial regulation. They called for an EU-wide ban on naked short-selling - a type of high-risk trading - and tight controls on credit default swaps.
However the Commission appears to have rejected that demand in a draft od new laws presented on Monday, Reuters reported.
A new EU strategy for jobs and growth - called the 2020 strategy - will also be discussed at the EU summit in Brussels.