Barroso said: "Yes there is turbulence in the financial markets, [but] there is no need to rush for the life boats".
A joint news conference is scheduled for Tuesday evening, when the leaders are expected to agree that while the "fundamentals" of the European economy remain sound, institutional reform is needed to counter the effects of the global crisis.
A spokesman for Brown said: "There will be a number of specific issues they will be discussing, such as transparency of banks' balance sheets, cross-border co-operation to deal with financial crises, the role of credit ratings agencies and so on."
He said a meeting of finance ministers from the world's eight most industrialised nations next month is expected to take forward any specific proposals before the G8 meets in Japan in July.
Long on rhetoric?
Alistair Darling, Britain's finance minister, rejected claims in London's Financial Times that the talks could be "long on rhetoric and short on concrete outcomes, with disagreements among the leaders for the need for tighter regulation".
But there was concern in Italy and France about the implications for the EU as a whole about a mini-summit involving only the leaders of the 27-member bloc's four biggest economies.
Il Sole 24 Ore, Italy's business daily, said it could lead to a "multi-tier" EU, with the major economies taking separate decisions.
Francois Hollande, the head of France's Socialist party, told Europe 1 radio: "You don't sort out such an important issue with just four people."
Hollande said a meeting of all Europe's finance ministers was needed.
The talks come amid the continuing fallout from the crisis on the US sub-prime mortgage sector last year that saw a squeeze on the global credit markets.
The market turmoil, which triggered an emergency 75 point rate cut by the US central bank last week, has been compounded by a rogue trader scandal at France's Societe Generale bank and the near collapse of Britain's Northern Rock.
On Tuesday, stock markets in Asia and Europe rallied after an overnight rebound on Wall Street, recovering some of their recent heavy losses as investors pinned their hopes on another US interest rate cut, dealers said.
Brown will be looking to gain support for his plans to reform global institutions like the IMF and the World Bank, which he believe are now ill-suited to the modern, globalised world.
He said in a speech in India last Monday that the IMF should have an enhanced "surveillance" role, with the ability to assess and warn of potential economic crises.
British media suggested that Brown will also seek to use the meeting to demonstrate his commitment to Europe, after missing the formal signing with other leaders of the new EU treaty in Lisbon last month.