* Resignation of Portugal's PM steals summit agenda
* Lame duck Lisbon government rejects early bailout bid
* Euro zone bailout fund to be finalised only in June
* Germany gets delay in payments into permanent fund (Adds S&P ratings downgrade of Portugal in paragraph 10)
By Luke Baker and Noah Barkin
BRUSSELS, March 25 (Reuters) - European leaders agreed on Thursday to increase their financial rescue fund to the full 440 billion euros by June, but avoided discussion of Portugal which is under pressure to seek a bailout following the resignation of its prime minister.
Having said for weeks that they would agree a "comprehensive package" to tackle the euro zone debt crisis by the end of March, the leaders ended up delaying a final decision on boosting their safety net until mid-year.
That agreement at a two-day summit in Brussels was lauded as an accomplishment by Herman Van Rompuy, the president of the European Council, but worries about Portugal's political crisis overshadowed the meeting.
Prime Minister Jose Socrates quit on Wednesday after parliament rejected new austerity measures that he had hoped would allow the country to avoid following Greece and Ireland in needing to ask for EU/IMF financial assistance.
He is the second euro zone leader to fall victim to the rolling sovereign debt crisis after Ireland's prime minister was booted out of office last month.
Despite stepping down, Socrates came to the two-day summit and was warmly received by other leaders, diplomats said.
He resisted pressure from his peers to accept a bailout, however, and made it clear that he would hold that line, at least until a new Portuguese government is formed -- probably after early elections in about two months' time.
The fall of the government prompted Fitch to cut Portugal's credit rating by two notches to A-, saying risks to the country's financing had risen after parliament failed to pass fiscal consolidation measures.
The ratings agency warned further downgrades were likely in the next three to six months in the absence of a "timely and credible" EU/IMF support programme.
Standard & Poor's also cut Portugal's credit rating by two notches to BBB and said a further cut could follow as soon as next week depending on the shape of the euro zone bailout fund.
European Central Bank President Jean-Claude Trichet told reporters as he left the summit that it was crucial for Portugal to stick to the fiscal austerity measures Socrates had proposed.
EU diplomats said Socrates had privately reassured other leaders that no matter what sort of government emerges after new elections, it would stick to the austerity programme.
The Portuguese upheaval underscored the wealth of political obstacles the single currency bloc faces in trying to solve a debt crisis that has deepened over the past year.
Only a few days ago, the summit had been expected to deliver a full package that would reassure financial markets, but Thursday's decisions fell short of what some investors had expected only a few days ago.
IMF CONTAGION WORRIES
Senior euro zone officials said Portugal was likely to need 60-80 billion euros in assistance from the EU rescue fund and the International Monetary Fund. No talks have begun yet and will anyway have to wait until a new government is formed.
Portuguese benchmark 10-year bond yields hit new highs on Thursday, climbing to 7.90 percent, far above levels that economists say would allow Lisbon to service its debt long term.
Lisbon needs to refinance about 4.5 billion euros of debt in April and a similar amount in June, which may prove a trigger for finally making the request for aid.
One problem is that any bailout request would have to be approved by parliament and the majority is opposed to asking for help.
With Portugal widely expected to seek assistance, attention could soon shift to Spain, which has gradually won back the confidence of investors in recent months by unveiling reforms of the labour market and pension system, as well as a plan for shoring up its ailing savings banks.
In a sign that contagion worries remain, sources told Reuters in Washington that the head of the International Monetary Fund (IMF) would seek approval from member countries next week to activate a $580 billion crisis fund.
"The biggest worry is the high risk of contagion from Portugal and general global uncertainty will trigger a new wave of borrwing from the fund," one source said, noting that Spain held one-third of Portugal's public debt.
SHORT OF A DEAL?
While leaders agreed they would finalise the increase in the current bailout fund -- the European Financial Stability Facility -- by June, they still have to negotiate political hurdles in both Portugal and Finland to get that achieved.
They are also trying to put the finishing touches to the European Stability Mechanism, a permanent rescue fund that will replace the EFSF in mid-2013.
The ESM will have an effective capacity of 500 billion euros, including 80 billion euros of paid-in capital.
The original intention was to inject that capital in two tranches of 40 billion, but Germany secured a concession on Thursday and the total will now be paid in via five equal annual installments, beginning in July 2013. (Reporting by Marc Angrand, Rex Merrifield, Jan Strupczewski) (Writing by Noah Barkin, Luke Baker and Paul Taylor)