Eurozone finance ministers are meeting to discuss a bailout for Spain's banks, and the future of Greece's two rescue packages.
The ministers have already agreed to give indebted Spanish banks up to 100bn euros ($126bn; £81bn) of aid, but Madrid has to make a formal request.
The Spanish government said it would do this "in the coming days" after an audit of the banks.
Meanwhile, Greece has confirmed it wants to renegotiate its bailout terms.
Speaking to reporters as he arrived for the meeting in Luxembourg, Spain's Economy Minister Luis De Guindos said: "We have already started working on the design of the aid [for Spanish banks] with the Commission, the European Central Bank, and the International Monetary Fund."
As ministers were meeting, an independent audit of the country's banks was published, saying they needed up to 62bn euros ($78bn; £50bn) of bailout funds.
Although Greece's new coalition government had already pledged to renegotiate its two bailout deals, the formal statement was made by Greece's new Prime Minister Antonis Samaras.
He said the government wished to "revise the terms of the loan agreement without jeopardising the country's European course or its presence in the euro".
Greece would like to extend the term of the loans it is continuing to receive from the European Union and International Monetary Fund.
This would reduce the country's monthly payments and give economic reforms such as the lower minimum wage and more liberal work practices more time to generate the economic growth necessary to repay the country's huge debts.
France's Finance Minister Pierre Moscovici said: "We know that it means that Greece will have to respect its commitments.
"But it also means that Europe has to be sensitive to the feelings of the Greek people, and take measures in order to help the country achieve growth.
"Efforts must be made, but at the same time we have to create conditions for hope. That's what the euro must be about."
However, despite Mr Moscovici's warm words, most analysts say that Germany - the eurozone's biggest economy and largest individual financial contributor to the rescue funds - is yet to be convinced.
Dutch Finance Minister Jan Kees de Jager was also cautious about Greece's plans.
He said: "With smarter measures then you can realise more, that is better, but an alternative to hard, painful reform, that alternative is not there."
The continuing focus on Spain's banks, comes as the government's cost of borrowing - the yields on its bonds - hit a 16-year high.
Madrid sold 2.2bn euros (£1.7bn) of bonds repayable over two, three and five years.
It paid a yield of 6.07% on five year bonds, up from 4.96% in May.
The finance ministers are also facing increased calls to act to reduce the cost of government borrowing across the eurozone, by using the region's two main bailout funds, the European Financial Stability Facility (EFSF), and the new European Stability Mechanism (ESM) fund, to buy up sovereign bonds on the open market.
Belgian finance minister Steven Vanackere said a mix of short and long term measures were needed to tackle the crisis.
"We need two answers: in the short term, the here and now answer for Greece, for Spain, they are all in need, but also in the longer term perspective, the building blocks that [EU Council President] Herman van Rompuy and also [Euro Group head] Mr Juncker will outline at the end of the month.
"The combination of these should give the market confidence."
The constitutions of the EFSF, and the forthcoming ESM already allow both to lend money to governments.
In an interview with the Financial Times, Benoit Coere, a senior policy maker of the European Central Bank said: "Certainly it's a mystery why the EFSF was allowed almost a year ago to undertake secondary market interventions and governments have not yet chosen to use that possibility."
Providing a cheaper alternative to commercial bond markets would reduce the cost of financing government borrowing and enable countries such as Spain and Italy to meet strict targets on reducing total national debt.
In the longer term, eurozone leaders are moving towards a system of more integrated government finances and bank regulation which could prevent future sovereign debt or banking crises.
But, at this week's meeting of leaders from the world's 20 biggest economies, there seemed to be consensus that eurozone politicians will have to put in place interim measures such as a bond-buying scheme soon to prevent the current crisis from deepening.