Greece will probably default but will not leave the eurozone, Fitch credit ratings agency said on Tuesday, as pressure increased on the Greek government to push through with fiscal reforms.

International lenders told Greece on Monday it must shrink its public sector to avoid running out of money within weeks.

While widely expected, a Greek default would further unsettle already nervous financial markets, fuelling fears a precedent had been set for other struggling eurozone states and sending yields on other peripheral bonds sharply higher.

However, Fitch did not expect Greece to leave the eurozone, as some in markets have speculated in recent weeks.

"Concerns over the risk of a break-up of the eurozone are greatly exaggerated," David Riley, Fitch's head of global sovereign ratings said in a news release.

Fitch also said it did not expect any systematically important financial institution or sovereign to be allowed to default.

Contagion fears have put the spotlight on Italy and Spain's finances and yields on their benchmark bonds remain high despite austerity measures and regular European Central Bank purchases in the bond market over the past month.

Standard & Poor's, another ratings agency, cut Italy's credit ratings on Monday, pushing the Italian yield spread over Germany wider.

Worries the crisis could spread have also put pressure on larger eurozone economies such as France, whose banks are heavily exposed to peripheral debt.