America's new treasury secretary Jack Lew has demanded that Europe do more to grow its austerity-afflicted economy amid concerns that Portugal was heading towards its second international bailout.

Reflecting deep anxiety in the Obama regime about the risks posed by the single currency's prolonged double-dip recession, Lew used a visit to Brussels to urge expansionary measures.

"Our economy's strength remains sensitive to events beyond our shores and we have an immense stake in Europe's health and stability," Lew said. "The Unites States has no bigger, no more important economic relationship that it does with Europe."

Lew added: "I was particularly interested in our European partners' plans to strengthen sources of demand at a time of rising unemployment."

The call came as Germany's finance minister, Wolfgang Schäuble, insisted that Portugal must find news ways to make budget cuts after the country's constitutional court threw out measures designed to save money. "Portugal has made lots of progress in the last year to gain access to financial markets. But after this [constitutional court] decision it will have to find new measures."

Portugal has cut spending by €13bn (£11.1bn) – 8% of national output – since it was bailed out by the so-called troika of the European Union, the European Central Bank and the International Monetary Fund two years ago. Austerity has taken its toll on the economy, which shrank by more than 3% in 2012, and late last week the constitutional court ruled against plans to trim an additional €1.3bn from the budget this year through cuts in sick pay and unemployment benefit.

José Manuel Barroso, the European commission president, urged Europe's finance ministers to grant Portugal more time to meet the tough terms of its bail out loan after the prime minister Pedro Passos Coelho said he would make up the shortfall from savings in health and education budgets.

EU finance ministers are due to decide on requests from Portugal and Ireland to extend the maturities of their loans when they meet in Dublin on Friday and Saturday.

Barroso said he welcomed Portugal's reaffirmed commitment to making the cuts. "This is vital. It is vital in order to maintain and boost Portugal's credibility, and to enable the country to find under its own steam the funding its economy needs.

"As regards the next steps … we support extending the maturities of the loans granted to Portugal. But this is a decision which goes beyond our remit; it is a decision to be taken by the ministers of finance of all the eurozone governments. However, we do think this decision should be taken as soon as possible, and that it will improve Portugal's prospects of a return to the markets and enhance the credibility of the adjustment programme, thereby lending support to the remarkable efforts undertaken by Portugal in recent times, not least of which are the sacrifices made by the Portuguese people."

A finance ministry spokesman said the court decision would result in an unscheduled visit from the troika. "The court decision created an uncertainty which justifies this visit in-between reviews, as do the spending cuts that the government promised to present by the end of April or beginning of May."